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2.35k
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-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A385119
G.f. A(x) satisfies A(x) = 1 + 9*x*A(x)^(5/3).
[ "1", "9", "135", "2430", "48195", "1015740", "22320522", "505692720", "11727186075", "277005649635", "6641224015140", "161193712078854", "3953072078945730", "97801207953712200", "2438092322304120720", "61182608813245896840", "1544295394480280288715", "39180450803555268621540" ]
[ "nonn" ]
13
0
2
[ "A135864", "A214668", "A245114", "A385117", "A385119" ]
null
Seiichi Manyama, Jun 18 2025
2025-06-20T08:10:47
oeisdata/seq/A385/A385119.seq
61d46e6351038e9007ab08e0988b7912
A385120
Number of fixed tree-like polyedges on the square lattice with n edges, rooted at a vertex.
[ "1", "4", "18", "88", "435", "2184", "11018", "55888", "284229", "1448800", "7396290", "37804344", "193405121", "990117104", "5072380140" ]
[ "nonn", "more", "hard" ]
56
0
2
[ "A056841", "A066158", "A096267", "A308409", "A385120" ]
null
Ben Samberg, Jun 18 2025
2025-07-04T17:19:47
oeisdata/seq/A385/A385120.seq
b27f4c57e40004c4fa6880f413abafe9
A385121
a(n+1) = 12*a(n) - a(n-1), a(0) = a(1) = 2, a(n) = a(1-n).
[ "2", "2", "22", "262", "3122", "37202", "443302", "5282422", "62945762", "750066722", "8937854902", "106504192102", "1269112450322", "15122845211762", "180205030090822", "2147337515878102", "25587845160446402", "304906804409478722", "3633293807753298262", "43294618888630100422" ]
[ "nonn", "easy" ]
10
0
1
[ "A061292", "A077417", "A385121" ]
null
Michael Somos, Jun 18 2025
2025-06-18T23:18:26
oeisdata/seq/A385/A385121.seq
74de0af9981e4c5f6cb94686e1b5f2cf
A385122
a(n) = d(phi(n)) - phi(d(n)) where d(n) = A000005(n) is the number of divisors and phi(n) = A000010(n) is the Euler totient function.
[ "0", "0", "1", "0", "2", "0", "3", "1", "2", "1", "3", "1", "5", "2", "2", "0", "4", "2", "5", "2", "4", "2", "3", "0", "4", "4", "4", "4", "5", "0", "7", "3", "4", "3", "6", "0", "8", "4", "6", "1", "7", "2", "7", "4", "6", "2", "3", "1", "6", "4", "4", "6", "5", "2", "6", "4", "7", "4", "3", "1", "11", "6", "7", "0", "8", "2", "7", "4", "4", "4", "7", "4", "11", "7", "6", "7", "10", "4", "7", "2", "4", "6", "3", "4", "5", "6" ]
[ "sign" ]
12
1
5
[ "A000005", "A000010", "A062821", "A078148", "A078150", "A163109", "A385122" ]
null
Sean A. Irvine, Jun 18 2025
2025-06-19T11:56:45
oeisdata/seq/A385/A385122.seq
1075fdc94eb23ee3f0ac3dac5832c10c
A385123
Triangle Read by rows: T(n,k) is the number of rooted ordered trees with n non-root nodes with non-root node labels in {1,..,k} such that all labels appear at least once in all groups of sibling nodes.
[ "1", "0", "1", "0", "2", "2", "0", "5", "6", "6", "0", "14", "22", "36", "24", "0", "42", "90", "150", "240", "120", "0", "132", "378", "648", "1560", "1800", "720", "0", "429", "1638", "3318", "8400", "16800", "15120", "5040", "0", "1430", "7278", "18180", "43128", "126000", "191520", "141120", "40320", "0", "4862", "32946", "98502", "238320", "834120", "1905120", "2328480", "1451520", "362880" ]
[ "nonn", "tabl" ]
7
0
5
[ "A000108", "A000142", "A107429", "A384685", "A384747", "A385123", "A385125" ]
null
John Tyler Rascoe, Jun 18 2025
2025-06-22T03:11:35
oeisdata/seq/A385/A385123.seq
d22ecec681cc5f10401c7cbe0d563453
A385124
Numbers k such that there are exactly 7 primes between 30*k and 30*k+30.
[ "1", "2", "49", "62", "79", "89", "188", "6627", "9491", "18674", "22621", "31982", "34083", "38226", "38520", "41545", "48713", "53887", "89459", "103205", "114731", "123306", "139742", "140609", "149125", "168237", "175125", "210554", "223949", "229269", "237794", "240007", "267356", "288467", "321451", "364921", "368248", "373370", "391701" ]
[ "nonn" ]
40
1
2
[ "A000720", "A098592", "A100418", "A100419", "A100420", "A100421", "A100422", "A100423", "A385124" ]
null
Jianglin Luo, Jun 18 2025
2025-06-24T15:33:50
oeisdata/seq/A385/A385124.seq
ce9d49824b1f6e3d38be32ae89ba210d
A385125
Number of rooted ordered trees with n non-root nodes all labeled with numbers greater than 0 such that the labels of all groups of sibling nodes cover the same initial interval.
[ "1", "1", "4", "17", "96", "642", "5238", "50745", "568976", "7256750", "103622742", "1634819518", "28208152974", "528060735100", "10654676857578" ]
[ "nonn", "more" ]
11
0
3
[ "A000108", "A107429", "A384685", "A384747", "A385123", "A385125" ]
null
John Tyler Rascoe, Jun 18 2025
2025-06-22T03:11:30
oeisdata/seq/A385/A385125.seq
0ad024f011cc6fe68dd75aadca1872fd
A385126
Hereditarily evil prime powers: numbers of the form p^k where p is prime and p^j is evil for 1 <= j <= k.
[ "3", "5", "9", "17", "23", "27", "29", "43", "53", "71", "83", "89", "101", "113", "139", "149", "163", "197", "257", "263", "269", "277", "281", "293", "311", "317", "337", "347", "349", "353", "359", "373", "383", "389", "401", "449", "461", "467", "479", "503", "509", "523", "547", "571", "593", "599", "619", "643", "673", "683", "691", "739", "751", "773", "797", "811", "821", "839", "853", "857", "863", "881" ]
[ "nonn", "base" ]
9
1
1
[ "A001969", "A027699", "A385126" ]
null
Robert Israel, Jun 18 2025
2025-06-25T00:44:59
oeisdata/seq/A385/A385126.seq
e827072bbbbfab009f6179920cc1b2f9
A385127
Consecutive internal states of the linear congruential pseudo-random number generator for gcc 2.6.3 when started at 1.
[ "1", "69074", "475904815", "884950952", "997714317", "2674863854", "2153294491", "4064640292", "103025113", "3375687626", "3068976839", "1640333408", "3540823269", "1389565030", "527860659", "3125448028", "2218581681", "3669905602", "625116511", "3161038872", "3721292605", "2231040222", "880447435" ]
[ "nonn", "easy" ]
11
1
2
[ "A084276", "A096552", "A385127" ]
null
Sean A. Irvine, Jun 18 2025
2025-06-23T19:38:09
oeisdata/seq/A385/A385127.seq
dec7800dadd769c1e147cf20c34ba608
A385128
The number of divisors of n whose maximum exponent in their prime factorization is even.
[ "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "3", "1", "1", "1", "3", "1", "3", "1", "3", "1", "1", "1", "3", "2", "1", "2", "3", "1", "1", "1", "3", "1", "1", "1", "6", "1", "1", "1", "3", "1", "1", "1", "3", "3", "1", "1", "5", "2", "3", "1", "3", "1", "3", "1", "3", "1", "1", "1", "5", "1", "1", "3", "4", "1", "1", "1", "3", "1", "1", "1", "6", "1", "1", "3", "3", "1", "1", "1", "5", "3", "1", "1", "5", "1", "1", "1" ]
[ "nonn", "easy" ]
9
1
4
[ "A000005", "A001221", "A001620", "A051903", "A368714", "A383156", "A385128", "A385129", "A385130" ]
null
Amiram Eldar, Jun 24 2025
2025-06-25T01:26:26
oeisdata/seq/A385/A385128.seq
01e98a4a955c771931d438116c5bf827
A385129
The number of divisors of n whose maximum exponent in their prime factorization is odd.
[ "0", "1", "1", "1", "1", "3", "1", "2", "1", "3", "1", "3", "1", "3", "3", "2", "1", "3", "1", "3", "3", "3", "1", "5", "1", "3", "2", "3", "1", "7", "1", "3", "3", "3", "3", "3", "1", "3", "3", "5", "1", "7", "1", "3", "3", "3", "1", "5", "1", "3", "3", "3", "1", "5", "3", "5", "3", "3", "1", "7", "1", "3", "3", "3", "3", "7", "1", "3", "3", "7", "1", "6", "1", "3", "3", "3", "3", "7", "1", "5", "2", "3", "1", "7", "3", "3", "3" ]
[ "nonn", "easy" ]
10
1
6
[ "A000005", "A001221", "A001620", "A051903", "A368714", "A383156", "A385128", "A385129", "A385131" ]
null
Amiram Eldar, Jun 24 2025
2025-06-25T01:26:33
oeisdata/seq/A385/A385129.seq
c8b9f5aef827c1537bbe6c5e9d99ef4a
A385130
The sum of divisors of n whose maximum exponent in their prime factorization is even.
[ "1", "1", "1", "5", "1", "1", "1", "5", "10", "1", "1", "17", "1", "1", "1", "21", "1", "28", "1", "25", "1", "1", "1", "17", "26", "1", "10", "33", "1", "1", "1", "21", "1", "1", "1", "80", "1", "1", "1", "25", "1", "1", "1", "49", "55", "1", "1", "81", "50", "76", "1", "57", "1", "28", "1", "33", "1", "1", "1", "97", "1", "1", "73", "85", "1", "1", "1", "73", "1", "1", "1", "80", "1", "1", "101", "81", "1", "1" ]
[ "nonn", "easy" ]
10
1
4
[ "A000203", "A001221", "A013661", "A051903", "A368714", "A383156", "A385128", "A385130", "A385131" ]
null
Amiram Eldar, Jun 24 2025
2025-06-24T06:15:13
oeisdata/seq/A385/A385130.seq
0e4637c41334ed9925ba0eff7c33cf15
A385131
The sum of divisors of n whose maximum exponent in their prime factorization is odd.
[ "0", "2", "3", "2", "5", "11", "7", "10", "3", "17", "11", "11", "13", "23", "23", "10", "17", "11", "19", "17", "31", "35", "23", "43", "5", "41", "30", "23", "29", "71", "31", "42", "47", "53", "47", "11", "37", "59", "55", "65", "41", "95", "43", "35", "23", "71", "47", "43", "7", "17", "71", "41", "53", "92", "71", "87", "79", "89", "59", "71", "61", "95", "31", "42", "83", "143", "67", "53" ]
[ "nonn", "easy" ]
10
1
2
[ "A000203", "A001221", "A013661", "A051903", "A368714", "A383156", "A385129", "A385130", "A385131" ]
null
Amiram Eldar, Jun 24 2025
2025-06-24T06:15:22
oeisdata/seq/A385/A385131.seq
376a09997a3777cb4515393317a1acc9
A385132
The number of integers k from 1 to n such that gcd(n, k) has an even maximum exponent in its prime factorization.
[ "1", "1", "2", "3", "4", "2", "6", "5", "7", "4", "10", "7", "12", "6", "8", "11", "16", "8", "18", "13", "12", "10", "22", "11", "21", "12", "20", "19", "28", "8", "30", "21", "20", "16", "24", "24", "36", "18", "24", "21", "40", "12", "42", "31", "29", "22", "46", "25", "43", "22", "32", "37", "52", "22", "40", "31", "36", "28", "58", "31", "60", "30", "43", "43", "48", "20", "66", "49", "44" ]
[ "nonn", "easy" ]
11
1
3
[ "A001221", "A051903", "A368714", "A384655", "A385132", "A385133" ]
null
Amiram Eldar, Jun 24 2025
2025-06-25T01:26:01
oeisdata/seq/A385/A385132.seq
e4297821f5f24d3d63037c31514c4a5d
A385133
The number of integers k from 1 to n such that gcd(n, k) has an odd maximum exponent in its prime factorization.
[ "0", "1", "1", "1", "1", "4", "1", "3", "2", "6", "1", "5", "1", "8", "7", "5", "1", "10", "1", "7", "9", "12", "1", "13", "4", "14", "7", "9", "1", "22", "1", "11", "13", "18", "11", "12", "1", "20", "15", "19", "1", "30", "1", "13", "16", "24", "1", "23", "6", "28", "19", "15", "1", "32", "15", "25", "21", "30", "1", "29", "1", "32", "20", "21", "17", "46", "1", "19", "25", "46", "1", "33", "1", "38", "32" ]
[ "nonn", "easy" ]
12
1
6
[ "A001221", "A051903", "A368714", "A384655", "A385132", "A385133" ]
null
Amiram Eldar, Jun 24 2025
2025-06-25T01:26:16
oeisdata/seq/A385/A385133.seq
cd918ceb4d43daadec817ec70e42e04a
A385134
The sum of divisors d of n such that n/d is a biquadratefree number (A046100).
[ "1", "3", "4", "7", "6", "12", "8", "15", "13", "18", "12", "28", "14", "24", "24", "30", "18", "39", "20", "42", "32", "36", "24", "60", "31", "42", "40", "56", "30", "72", "32", "60", "48", "54", "48", "91", "38", "60", "56", "90", "42", "96", "44", "84", "78", "72", "48", "120", "57", "93", "72", "98", "54", "120", "72", "120", "80", "90", "60", "168", "62", "96", "104", "120", "84", "144" ]
[ "nonn", "easy", "mult" ]
12
1
2
[ "A000203", "A001615", "A002131", "A008683", "A046100", "A069208", "A076752", "A129527", "A244963", "A254981", "A307430", "A327626", "A385006", "A385134", "A385135", "A385136", "A385137", "A385138", "A385139" ]
null
Amiram Eldar, Jun 19 2025
2025-06-20T08:09:32
oeisdata/seq/A385/A385134.seq
0beb13afa8e1462db2cd2c8502b966a2
A385135
The sum of divisors d of n such that n/d is an exponentially odd number (A268335).
[ "1", "3", "4", "6", "6", "12", "8", "13", "12", "18", "12", "24", "14", "24", "24", "26", "18", "36", "20", "36", "32", "36", "24", "52", "30", "42", "37", "48", "30", "72", "32", "53", "48", "54", "48", "72", "38", "60", "56", "78", "42", "96", "44", "72", "72", "72", "48", "104", "56", "90", "72", "84", "54", "111", "72", "104", "80", "90", "60", "144", "62", "96", "96", "106", "84", "144" ]
[ "nonn", "easy", "mult" ]
9
1
2
[ "A001615", "A002131", "A013662", "A033634", "A069208", "A076752", "A129527", "A244963", "A254981", "A268335", "A327626", "A385134", "A385135", "A385136", "A385137", "A385138", "A385139" ]
null
Amiram Eldar, Jun 19 2025
2025-06-20T08:09:29
oeisdata/seq/A385/A385135.seq
7178a00e88910f2f25ea2b46a012e49f
A385136
The sum of divisors d of n such that n/d is a cubefull number (A036966).
[ "1", "2", "3", "4", "5", "6", "7", "9", "9", "10", "11", "12", "13", "14", "15", "19", "17", "18", "19", "20", "21", "22", "23", "27", "25", "26", "28", "28", "29", "30", "31", "39", "33", "34", "35", "36", "37", "38", "39", "45", "41", "42", "43", "44", "45", "46", "47", "57", "49", "50", "51", "52", "53", "56", "55", "63", "57", "58", "59", "60", "61", "62", "63", "79", "65", "66", "67", "68" ]
[ "nonn", "easy", "mult" ]
10
1
2
[ "A001615", "A002131", "A013661", "A036966", "A069208", "A076752", "A129527", "A244963", "A254981", "A327626", "A385005", "A385134", "A385135", "A385136", "A385137", "A385138", "A385139" ]
null
Amiram Eldar, Jun 19 2025
2025-06-20T08:09:25
oeisdata/seq/A385/A385136.seq
fa6c180494c6e74873a82522176c2a99
A385137
The sum of divisors d of n such that n/d is a 3-smooth number (A003586).
[ "1", "3", "4", "7", "5", "12", "7", "15", "13", "15", "11", "28", "13", "21", "20", "31", "17", "39", "19", "35", "28", "33", "23", "60", "25", "39", "40", "49", "29", "60", "31", "63", "44", "51", "35", "91", "37", "57", "52", "75", "41", "84", "43", "77", "65", "69", "47", "124", "49", "75", "68", "91", "53", "120", "55", "105", "76", "87", "59", "140", "61", "93", "91", "127", "65", "132" ]
[ "nonn", "easy", "mult" ]
8
1
2
[ "A001615", "A002131", "A003586", "A064987", "A069208", "A072044", "A072045", "A072079", "A076752", "A129527", "A244963", "A254981", "A327626", "A385134", "A385135", "A385136", "A385137", "A385138", "A385139" ]
null
Amiram Eldar, Jun 19 2025
2025-06-20T08:09:21
oeisdata/seq/A385/A385137.seq
377e2d1918195eba223de2957f7b393e
A385138
The sum of divisors d of n such that n/d is a 5-rough number (A007310).
[ "1", "2", "3", "4", "6", "6", "8", "8", "9", "12", "12", "12", "14", "16", "18", "16", "18", "18", "20", "24", "24", "24", "24", "24", "31", "28", "27", "32", "30", "36", "32", "32", "36", "36", "48", "36", "38", "40", "42", "48", "42", "48", "44", "48", "54", "48", "48", "48", "57", "62", "54", "56", "54", "54", "72", "64", "60", "60", "60", "72", "62", "64", "72", "64", "84", "72", "68", "72" ]
[ "nonn", "easy", "mult" ]
8
1
2
[ "A001615", "A002131", "A007310", "A013661", "A064987", "A069208", "A072044", "A072045", "A076752", "A129527", "A186099", "A244963", "A254981", "A327626", "A385134", "A385135", "A385136", "A385137", "A385138", "A385139" ]
null
Amiram Eldar, Jun 19 2025
2025-06-20T08:09:43
oeisdata/seq/A385/A385138.seq
80dcf2a09f0a72b847355721bb508acd
A385139
The sum of divisors d of n such that n/d has exponents in its prime factorization that are all powers of 2 (A138302).
[ "1", "3", "4", "7", "6", "12", "8", "14", "13", "18", "12", "28", "14", "24", "24", "29", "18", "39", "20", "42", "32", "36", "24", "56", "31", "42", "39", "56", "30", "72", "32", "58", "48", "54", "48", "91", "38", "60", "56", "84", "42", "96", "44", "84", "78", "72", "48", "116", "57", "93", "72", "98", "54", "117", "72", "112", "80", "90", "60", "168", "62", "96", "104", "116", "84", "144" ]
[ "nonn", "mult", "easy" ]
8
1
2
[ "A001615", "A002131", "A004709", "A069208", "A076752", "A129527", "A138302", "A244963", "A254981", "A327626", "A353900", "A385134", "A385135", "A385136", "A385137", "A385138", "A385139" ]
null
Amiram Eldar, Jun 19 2025
2025-06-20T08:09:47
oeisdata/seq/A385/A385139.seq
c6d9fd4bd74d27297a0a459eee7e185c
A385140
E.g.f. A(x) satisfies A(x) = exp(2*x*A(-x)^(1/2)).
[ "1", "2", "0", "-22", "-16", "1042", "1792", "-116758", "-330496", "24101090", "96518144", "-7976308118", "-41609056256", "3875582805746", "25008143335424", "-2601876338050582", "-20048671462064128", "2308957345471798978", "20711293319504723968", "-2618684079639256157974", "-26823633677081126109184" ]
[ "sign" ]
14
0
2
[ "A141369", "A360987", "A385140", "A385141" ]
null
Seiichi Manyama, Jun 19 2025
2025-06-19T10:24:21
oeisdata/seq/A385/A385140.seq
37fcb5d6414896a0a85f27936f09a02a
A385141
E.g.f. A(x) satisfies A(x) = exp(3*x*A(-x)^(1/3)).
[ "1", "3", "3", "-36", "-147", "1728", "14391", "-193344", "-2572263", "39702528", "744878859", "-13061956608", "-320684319675", "6310454624256", "192965057926335", "-4214431981191168", "-155017339047231951", "3722456794316931072", "160513751565607780755", "-4204149732317088448512" ]
[ "sign" ]
14
0
2
[ "A141369", "A360988", "A385140", "A385141" ]
null
Seiichi Manyama, Jun 19 2025
2025-06-19T10:24:30
oeisdata/seq/A385/A385141.seq
debf1039068438f97134e441f87a17be
A385142
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5) with a(1) = a(2) = a(3) = 0, a(4) = 1, and a(5) = 3.
[ "0", "0", "0", "1", "3", "6", "10", "15", "22", "35", "64", "129", "265", "529", "1013", "1873", "3394", "6126", "11148", "20552", "38303", "71760", "134408", "250880", "466361", "864339", "1600062", "2963186", "5494247", "10200142", "18952107", "35221440", "65442625", "121544393", "225655617", "418857277", "777451793", "1443184210", "2679343966" ]
[ "nonn", "easy" ]
13
1
5
[ "A017827", "A385142" ]
null
Hung Viet Chu, Jun 19 2025
2025-06-28T01:00:01
oeisdata/seq/A385/A385142.seq
c24765a5b2988b71fe60b671b23d649c
A385143
Number of minimum connected dominating sets in the n X n X n grid graph.
[ "1", "30", "75", "336" ]
[ "nonn", "more" ]
4
1
2
null
null
Eric W. Weisstein, Jun 19 2025
2025-06-21T11:49:04
oeisdata/seq/A385/A385143.seq
369f4c42723df458a9ae43f0a083f4f2
A385144
a(n) is the smallest 2*n + 1 digit prime consisting of a string of 2*n - 1 identical digits d sandwiched between two same digits different from d, or -1 if no such prime exists.
[ "101", "13331", "1333331", "188888881", "74444444447", "1666666666661", "188888888888881", "16666666666666661", "1666666666666666661", "155555555555555555551", "75555555555555555555557", "-1", "-1", "72222222222222222222222222227", "3111111111111111111111111111113", "155555555555555555555555555555551" ]
[ "sign", "base" ]
25
1
1
[ "A384979", "A385144" ]
null
Jean-Marc Rebert, Jun 19 2025
2025-06-25T10:34:44
oeisdata/seq/A385/A385144.seq
b65ecec5b742f3fb5968cdc8c2f4810d
A385145
Integers without 0 as a digit, with an odd number of digits, that are not repdigits, and such that the 2 products [d_1 d_2...dk]*[d_k+1 d_k+2...d_2k+1] and [d_1 d_2...d_k+1]*[d_k+2 d_k+2...d_2k+1] are equal.
[ "164", "195", "265", "498", "16664", "19995", "21775", "24996", "26665", "49998", "1249992", "1666664", "1999995", "2177775", "2499996", "2666665", "4999998", "124999992", "166666664", "199999995", "217777775", "249999996", "266666665", "499999998", "12499999992", "16666666664", "19999999995", "21777777775", "24999999996", "26666666665" ]
[ "nonn", "base" ]
19
1
1
[ "A052382", "A385145" ]
null
Michel Marcus, Jun 19 2025
2025-06-20T13:42:42
oeisdata/seq/A385/A385145.seq
77b17bea12d0629527813bb975db1a4f
A385147
a(n) = Sum_{i=1..n} 2^phi(i), where phi=A000010.
[ "2", "4", "8", "12", "28", "32", "96", "112", "176", "192", "1216", "1232", "5328", "5392", "5648", "5904", "71440", "71504", "333648", "333904", "338000", "339024", "4533328", "4533584", "5582160", "5586256", "5848400", "5852496", "274287952", "274288208", "1348030032", "1348095568", "1349144144", "1349209680", "1365986896", "1365990992" ]
[ "nonn", "easy" ]
15
1
1
[ "A000010", "A066781", "A385147" ]
null
Hunter Yeoman, Jun 19 2025
2025-07-02T21:15:01
oeisdata/seq/A385/A385147.seq
54a9a7f0035d26adb1f7ff77bbaf860e
A385148
a(n) = A001065(A346878(n)).
[ "0", "1", "6", "1", "7", "15", "8", "9", "11", "14", "10", "55", "15", "28", "54", "1", "22", "17", "14", "43", "66", "50", "16", "64", "1", "26", "78", "63", "31", "172", "20", "41", "90", "32", "40", "45", "50", "63", "144", "56", "40", "196", "26", "76", "259", "64", "43", "236", "1", "65", "126", "56", "64", "136", "56", "134", "186", "50", "34", "504", "63", "117", "198", "1", "64", "300", "74", "70", "222", "203" ]
[ "nonn" ]
22
1
3
[ "A001065", "A346878", "A377766", "A384411", "A385148" ]
null
Michel Marcus, Jun 19 2025
2025-06-24T07:20:38
oeisdata/seq/A385/A385148.seq
ff029abc0d96b6a9d2f5ff990813c8dd
A385149
Number of chiral pairs of asymmetric polyominoes with n cells of the regular tiling with Schläfli symbol {4,oo}.
[ "0", "0", "0", "0", "1", "8", "43", "225", "1162", "6081", "32315", "174856", "961764", "5369567", "30373643", "173811011", "1004802212", "5861460314", "34468644574", "204161097084", "1217143092549", "7299002607829", "44005589820244", "266608357403244", "1622502342468552", "9914884364399700" ]
[ "nonn", "easy" ]
9
0
6
[ "A001764", "A005034", "A005036", "A047749", "A369315", "A385149" ]
null
Robert A. Russell, Jun 19 2025
2025-06-22T00:17:30
oeisdata/seq/A385/A385149.seq
0b739d2dfadba2892af2f2693bce85da
A385150
Smallest starting x which reaches the Antihydra halting condition for the first time at 3*n+1 terms of the iteration x -> floor(3*x/2).
[ "1", "6", "10", "30", "24", "46", "14", "16", "1284", "2398", "1844", "1326", "1048", "466", "1822", "810", "5826", "856", "254", "2820", "42658", "1880", "21442", "1396", "414", "354130", "73370", "311112", "87492", "72154", "195408", "130272", "230286", "227214", "1668076", "927548", "2422042", "311516", "4138178", "1243802" ]
[ "nonn" ]
43
0
2
[ "A001764", "A032766", "A385150" ]
null
Roman Khrabrov, Jun 19 2025
2025-06-29T06:27:14
oeisdata/seq/A385/A385150.seq
db23cea7120b471e23dcb0a0751bf138
A385151
a(n) is the least possible difference between the largest and smallest volumes of distinct three-cuboid combination filling an n X n X n cube.
[ "6", "24", "20", "48", "42", "80", "54", "140", "99", "192", "143", "252", "150", "352", "238", "432", "304", "520", "294", "660", "437", "768", "525", "884", "486", "1064", "696", "1200", "806", "1344", "726", "1564", "1015", "1728", "1147", "1900", "1014", "2160", "1394", "2352", "1548", "2552", "1350", "2852", "1833", "3072", "2009", "3300", "1734" ]
[ "nonn", "new" ]
34
3
1
[ "A276523", "A381847", "A385151" ]
null
Janaka Rodrigo, Jun 19 2025
2025-07-16T23:34:56
oeisdata/seq/A385/A385151.seq
7d6505e8a3a621248f631e2b8fadf648
A385152
Pentagonal numbers that are one-fifth of another pentagonal number.
[ "0", "1", "2262", "11017977685", "24316671758562", "118442787685171571497", "261403178754290105125230", "1273254889025744028795358122877", "2810072963163120003620778537378426", "13687435462403616663579190345877254457425", "30208163863695025530402450846321663951473670" ]
[ "nonn", "new" ]
22
1
3
[ "A000326", "A385146", "A385152" ]
null
Kelvin Voskuijl, Jun 19 2025
2025-07-08T19:02:31
oeisdata/seq/A385/A385152.seq
c46475c8e77b36370d2685fabe552b59
A385153
a(n) is the least possible difference between the largest and smallest volumes of distinct four-cuboid combinations filling an n X n X n cube.
[ "5", "16", "16", "36", "30", "60", "48", "100", "83", "96", "123", "182", "130", "264", "182", "324", "224", "280", "259", "484", "369", "576", "449", "676", "423", "560", "528", "900", "598", "1008", "638", "1054", "859", "864", "979", "1330", "884", "1620", "1054", "1764", "1152", "1364", "1185", "2116", "1553", "2304", "1713", "2500", "1513", "1924", "1760" ]
[ "nonn", "new" ]
30
3
1
[ "A276523", "A384311", "A385153" ]
null
Janaka Rodrigo, Jun 19 2025
2025-07-16T23:35:05
oeisdata/seq/A385/A385153.seq
1705410de7cc92664ff6f5e07eef145e
A385155
Numbers z such that there exist two integers 0<x<y<z such that (1/sigma(x) + 1/sigma(y) + 1/sigma(z))*(x + y + z) = 3.
[ "1380", "1540", "1560", "1638", "2016", "2250", "2520", "2556", "2700", "2772", "3024", "3120", "3312", "3360", "3408", "3480", "3640", "3654", "3780", "3816", "3828", "3876", "4200", "4320", "4440", "4452", "4620", "4920", "4956", "5220", "5280", "5292", "5304", "5340", "5400", "5460", "5472", "5640", "5700", "5724", "5760", "5940", "6048", "6060", "6180" ]
[ "nonn", "hard" ]
24
1
1
[ "A000203", "A125492", "A384487", "A384814", "A385155" ]
null
S. I. Dimitrov, Jun 19 2025
2025-06-25T11:03:14
oeisdata/seq/A385/A385155.seq
1b3135e87a8b705030344fc3b37f52ce
A385157
Numbers k so that the binary expansion of 3^k starts with the binary expansion of k.
[ "1", "2", "3", "9", "27", "65", "95", "123", "163", "303", "451", "597", "760", "1757", "2546", "2700", "7142", "25030", "25719", "25772", "49105", "61426", "90981", "107497", "194210", "659077", "6732590", "8513462", "9344030", "14549893", "32276115", "89912342", "181720904", "280120681", "437484689", "896754175", "10625891495", "30605576222" ]
[ "nonn", "base" ]
43
1
2
[ "A000244", "A004656", "A385157" ]
null
Jayde S. Massmann, Jun 19 2025
2025-06-27T04:14:04
oeisdata/seq/A385/A385157.seq
93ccff9c7b8d4e9b764a5bd3c964008e
A385163
Let p = A002145(n) be the n-th prime == 3 (mod 4); a(n) is the multiplicative order of 1+-i modulo p in Gaussian integers.
[ "8", "24", "40", "72", "88", "40", "56", "184", "232", "264", "280", "312", "328", "408", "424", "56", "520", "552", "120", "648", "664", "712", "760", "792", "840", "296", "904", "952", "200", "1048", "1080", "376", "408", "1240", "120", "1384", "1432", "1464", "1512", "1528", "1672", "344", "584", "1768", "1848", "1864", "1912", "1944", "1960", "664", "2008", "2088", "2184", "2248", "456" ]
[ "nonn", "easy" ]
16
1
1
[ "A002145", "A384164", "A385163", "A385165" ]
null
Jianing Song, Jun 20 2025
2025-06-20T12:42:32
oeisdata/seq/A385/A385163.seq
50eac41f3fbb03fbb3d7c6470879428a
A385164
Let p = A002145(n) be the n-th prime == 3 (mod 4); 8*a(n) is the multiplicative order of 1+-i modulo p in Gaussian integers.
[ "1", "3", "5", "9", "11", "5", "7", "23", "29", "33", "35", "39", "41", "51", "53", "7", "65", "69", "15", "81", "83", "89", "95", "99", "105", "37", "113", "119", "25", "131", "135", "47", "51", "155", "15", "173", "179", "183", "189", "191", "209", "43", "73", "221", "231", "233", "239", "243", "245", "83", "251", "261", "273", "281", "57", "293", "299", "303", "309", "45", "107", "323", "329", "11", "115" ]
[ "nonn", "easy" ]
14
1
2
[ "A002145", "A385163", "A385164" ]
null
Jianing Song, Jun 20 2025
2025-06-20T15:07:38
oeisdata/seq/A385/A385164.seq
f12bce30108325b15b2074096b8a83f5
A385165
Let p = A002145(n) be the n-th prime == 3 (mod 4); a(n) is the multiplicative order of 2+-i modulo p in Gaussian integers.
[ "8", "48", "30", "180", "528", "96", "1848", "2208", "1740", "1496", "360", "1560", "2296", "10608", "11448", "5376", "4290", "1932", "11400", "8856", "27888", "16020", "1216", "3300", "3710", "49728", "51528", "14280", "3150", "69168", "7344", "80088", "8568", "48360", "13695", "40136", "6444", "44896", "7980", "146688", "29260", "92880", "48180" ]
[ "nonn", "easy" ]
22
1
1
[ "A002145", "A211241", "A385163", "A385165", "A385166" ]
null
Jianing Song, Jun 20 2025
2025-06-21T19:59:14
oeisdata/seq/A385/A385165.seq
54323871e7aca78de20eadc54bd0bb7a
A385166
Let p = A002145(n) be the n-th prime == 3 (mod 4); a(n) = (p+1) * ord(5,p) / ord(2+-i,p) = (p+1) * ord(5,p) / A385165(n). Here ord(a,m) is the multiplicative order of a modulo m.
[ "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "1", "1", "1", "2", "5", "1", "1", "1", "1", "3", "2", "2", "1", "1", "2", "2", "1", "1", "1", "11", "1", "4", "3", "10", "1", "1", "1", "3", "1", "2", "1", "1", "1", "6", "1", "6", "1", "3", "1", "1", "1", "4", "3", "24", "1", "1", "1", "1", "1", "3", "1", "4", "2", "1", "1", "1", "1", "1", "2", "1", "1", "8", "1", "27", "1", "1", "1", "1", "20", "3", "1", "4", "1", "1" ]
[ "nonn", "easy" ]
17
1
3
[ "A002145", "A211450", "A385165", "A385166", "A385167", "A385168", "A385180" ]
null
Jianing Song, Jun 20 2025
2025-06-21T19:59:56
oeisdata/seq/A385/A385166.seq
3ba0d45b61c652f58ce006fbf298dcaf
A385167
Primes p == 3 (mod 4) such that (p+1) * ord(5,p) / ord(2+-i,p) is even. Here ord(a,m) is the multiplicative order of a modulo m.
[ "11", "79", "131", "199", "211", "239", "251", "331", "359", "439", "479", "491", "571", "599", "691", "719", "811", "839", "919", "971", "1039", "1051", "1091", "1171", "1279", "1291", "1319", "1399", "1439", "1451", "1531", "1559", "1571", "1759", "1811", "1879", "1931", "1999", "2011", "2039", "2131", "2239", "2251", "2371", "2399", "2411", "2531", "2719", "2731", "2851", "2879", "2971", "2999" ]
[ "nonn", "easy" ]
23
1
1
[ "A002145", "A122869", "A385165", "A385166", "A385167", "A385168", "A385180" ]
null
Jianing Song, Jun 20 2025
2025-06-23T14:41:34
oeisdata/seq/A385/A385167.seq
1ebe29be277b2d751fdd3a138e71478c
A385168
Primes p == 3 (mod 4) such that (p+1) * ord(5,p) / ord(2+-i,p) > 1. Here ord(a,m) is the multiplicative order of a modulo m.
[ "11", "79", "83", "131", "139", "191", "199", "211", "239", "251", "307", "331", "347", "359", "419", "439", "479", "491", "503", "571", "587", "599", "659", "691", "719", "811", "839", "863", "919", "947", "971", "1019", "1039", "1051", "1091", "1103", "1171", "1223", "1231", "1279", "1291", "1319", "1399", "1439", "1451", "1499", "1523", "1531", "1559", "1567", "1571", "1619", "1667", "1759" ]
[ "nonn", "easy" ]
20
1
1
[ "A002145", "A384948", "A385165", "A385166", "A385167", "A385168", "A385180" ]
null
Jianing Song, Jun 20 2025
2025-06-23T14:41:40
oeisdata/seq/A385/A385168.seq
3ff9e5b4c9df130ed88b1ec674b897b8
A385169
Primes p == 3 (mod 4) such that the multiplicative order of 2+-i modulo p in Gaussian integers (A385165) is odd.
[ "331", "571", "599", "691", "839", "971", "1051", "1171", "1291", "1451", "1571", "1879", "2131", "2411", "2971", "3251", "3331", "3491", "3571", "3691", "3851", "4051", "4091", "4211", "4651", "4679", "4691", "4919", "4931", "5051", "5171", "5479", "5531", "5651", "5839", "5851", "5879", "6011", "6599", "6679", "6691", "7079", "7211", "7331", "7691", "8011", "8039", "8171", "8731", "8839", "9011", "9371", "9811" ]
[ "nonn", "easy" ]
27
1
1
[ "A122869", "A385165", "A385167", "A385168", "A385169", "A385179", "A385180", "A385188", "A385192", "A385217" ]
null
Jianing Song, Jun 20 2025
2025-06-26T14:31:02
oeisdata/seq/A385/A385169.seq
6f9be9b4de77871b99fa21ae740d616c
A385170
a(n) is the integer part of the reciprocal of the distance of x_n from its nearest integer, where x_n is the n-th extrema of gamma(x).
[ "1", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5" ]
[ "nonn" ]
35
0
2
[ "A256687", "A374856", "A377506", "A385170" ]
null
Jwalin Bhatt, Jun 20 2025
2025-07-02T17:33:02
oeisdata/seq/A385/A385170.seq
ab7625e39f86fd19bbc2bc11bd3c8846
A385171
Perfect powers m^k whose decimal expansion begins with k and ends with m, where m and k are greater than 1.
[ "25", "59049", "78125", "13060694016", "17179869184", "19073486328125", "30514648531249", "53613724194557", "59120987373568", "65944160601201", "116490258898219", "324965351768751", "512908935546875", "21936950640377856", "371308922853718751", "578261433548013568", "913517247483640899" ]
[ "nonn", "base" ]
8
1
1
[ "A001597", "A003226", "A033819", "A051248", "A074250", "A378857", "A385171" ]
null
Gonzalo Martínez, Jun 20 2025
2025-06-25T11:03:06
oeisdata/seq/A385/A385171.seq
7f6bbfb2909cfe21931a6da9abbc93bf
A385173
Smallest number of vertices for which n nonisomorphic connected cubic symmetric graphs exist.
[ "2", "4", "20", "56", "182", "432", "168", "364", "1792", "816", "1024", "1344", "1296", "1536", "6840" ]
[ "nonn", "more", "hard" ]
4
0
1
[ "A059282", "A385173" ]
null
Eric W. Weisstein, Jun 20 2025
2025-06-21T11:49:00
oeisdata/seq/A385/A385173.seq
5e0bf4187ae86ab92985c49bf8ec9e26
A385175
Cubes using at most three distinct digits, not ending in 0.
[ "1", "8", "27", "64", "125", "216", "343", "512", "729", "1331", "2744", "3375", "46656", "238328", "778688", "1030301", "5177717", "7077888", "9393931", "700227072", "1003003001", "44474744007", "1000300030001", "1000030000300001", "1331399339931331", "3163316636166336", "1000003000003000001", "1000000300000030000001", "1000000030000000300000001" ]
[ "nonn", "base", "changed" ]
22
1
2
[ "A000578", "A018884", "A030292", "A155146", "A202940", "A385175" ]
null
Gonzalo Martínez, Jun 20 2025
2025-07-10T11:24:07
oeisdata/seq/A385/A385175.seq
a5e89723375c42b6a6e4829b44431554
A385177
a(n) = Sum_{k=1..n} ceiling(k/phi), where phi is the golden ratio (A001622).
[ "1", "3", "5", "8", "12", "16", "21", "26", "32", "39", "46", "54", "63", "72", "82", "92", "103", "115", "127", "140", "153", "167", "182", "197", "213", "230", "247", "265", "283", "302", "322", "342", "363", "385", "407", "430", "453", "477", "502", "527", "553", "579", "606", "634", "662", "691", "721", "751", "782", "813", "845", "878", "911", "945", "979", "1014", "1050", "1086", "1123" ]
[ "nonn", "easy" ]
12
1
2
[ "A001622", "A019446", "A183136", "A385177" ]
null
Paolo Xausa, Jun 20 2025
2025-06-21T11:24:41
oeisdata/seq/A385/A385177.seq
2f2ed79caf2088d0ab73162b388e2fa5
A385178
Triangle T(n,k) read by rows in which the n-th diagonal lists the n-th differences of A001047, 0 <= k <= n.
[ "0", "1", "1", "3", "4", "5", "7", "10", "14", "19", "15", "22", "32", "46", "65", "31", "46", "68", "100", "146", "211", "63", "94", "140", "208", "308", "454", "665", "127", "190", "284", "424", "632", "940", "1394", "2059", "255", "382", "572", "856", "1280", "1912", "2852", "4246", "6305", "511", "766", "1148", "1720", "2576", "3856", "5768", "8620", "12866", "19171" ]
[ "nonn", "tabl", "easy" ]
76
0
4
[ "A000225", "A001047", "A027649", "A028243", "A033484", "A036561", "A053209", "A053581", "A059268", "A081656", "A248216", "A291012", "A321003", "A385178" ]
null
Paul Curtz, Jun 20 2025
2025-06-28T17:56:20
oeisdata/seq/A385/A385178.seq
a68add7e10f0a6772d51e36dc6636caf
A385179
Primes p == 3 (mod 4) such that the multiplicative order of 2+-i modulo p in Gaussian integers (A385165) is congruent to 2 modulo 4.
[ "11", "131", "211", "251", "491", "811", "919", "1039", "1091", "1319", "1399", "1531", "1811", "1931", "2011", "2251", "2371", "2531", "2731", "2851", "3011", "3079", "3371", "3931", "4079", "4451", "4519", "4759", "5011", "5639", "6091", "6131", "6211", "6359", "6451", "6491", "6571", "6971", "7411", "7451", "7559", "7639", "8291", "8719", "8971", "9091", "9491", "9719", "9839", "9851", "9931" ]
[ "nonn", "easy" ]
23
1
1
[ "A122869", "A385165", "A385167", "A385168", "A385169", "A385179", "A385188", "A385218" ]
null
Jianing Song, Jun 20 2025
2025-06-22T21:32:32
oeisdata/seq/A385/A385179.seq
a4cea9a688770fce8576bc3054c6b39f
A385180
Primes p == 3 (mod 4) such that (p+1) * ord(5,p) / ord(2+-i,p) is divisible by 4. Here ord(a,m) is the multiplicative order of a modulo m.
[ "331", "571", "599", "691", "839", "919", "971", "1039", "1051", "1171", "1279", "1291", "1319", "1399", "1439", "1451", "1571", "1759", "1879", "2131", "2411", "2879", "2971", "3079", "3251", "3331", "3491", "3571", "3691", "3851", "4051", "4079", "4091", "4211", "4519", "4639", "4651", "4679", "4691", "4759", "4919", "4931", "5051", "5119", "5171", "5279", "5479", "5519", "5531" ]
[ "nonn", "easy" ]
25
1
1
[ "A002145", "A122869", "A385165", "A385166", "A385167", "A385168", "A385180" ]
null
Jianing Song, Jun 20 2025
2025-06-23T14:41:26
oeisdata/seq/A385/A385180.seq
183370d927d71c8ccda585ce5777b93d
A385181
Number of disconnected cubic symmetric graphs on 2n vertices.
[ "0", "0", "0", "1", "0", "2", "0", "2", "1", "2", "0", "3", "0", "2", "2", "3", "0", "3", "0", "5", "2", "1", "0", "5", "1", "2", "2", "4", "0", "6", "0", "4", "1", "1", "2", "5", "0", "2", "2", "7", "0", "5", "0", "2", "4", "1", "0", "7", "1", "5", "1", "3", "0", "4", "1", "8", "2", "1", "0", "10", "0", "2", "4", "5", "2", "2", "0", "2", "1", "6", "0", "8", "0", "2", "4", "3", "1", "4", "0", "9", "3", "1", "0", "11", "1" ]
[ "nonn" ]
5
1
6
[ "A059282", "A385181" ]
null
Eric W. Weisstein, Jun 20 2025
2025-06-21T11:48:56
oeisdata/seq/A385/A385181.seq
688f8bc65f46e3e514805cc656e0f70a
A385182
Values of u in the quartets (1,u,v,w); i.e., values of u for solutions to (1+u) = v*(v+w), in positive integers, with v>1, sorted by nondecreasing values of u; see Comments.
[ "5", "7", "9", "11", "11", "13", "14", "15", "17", "17", "19", "19", "20", "21", "23", "23", "23", "25", "26", "27", "27", "29", "29", "29", "31", "31", "32", "33", "34", "35", "35", "35", "37", "38", "39", "39", "39", "41", "41", "41", "43", "43", "44", "44", "45", "47", "47", "47", "47", "49", "49", "50", "51", "51", "53", "53", "53", "54", "55", "55", "55", "56", "57", "59", "59" ]
[ "nonn", "new" ]
27
1
1
[ "A056924", "A385182", "A385183", "A385184", "A385592", "A385593", "A385594", "A385595", "A385596", "A385597", "A385598", "A385599", "A385600" ]
null
Clark Kimberling, Jun 23 2025
2025-07-10T00:14:03
oeisdata/seq/A385/A385182.seq
a90bdc9116446599e42990cd4c77260c
A385183
The v sequence in quartets (1,u,v,w); see A385182.
[ "2", "2", "2", "2", "3", "2", "3", "2", "2", "3", "2", "4", "3", "2", "2", "3", "4", "2", "3", "2", "4", "2", "3", "5", "2", "4", "3", "2", "5", "2", "3", "4", "2", "3", "2", "4", "5", "2", "3", "6", "2", "4", "3", "5", "2", "2", "3", "4", "6", "2", "5", "3", "2", "4", "2", "3", "6", "5", "2", "4", "7", "3", "2", "2", "3", "4", "5", "6", "2", "3", "7", "2", "4", "5", "2", "3", "6", "2", "4", "3", "2", "5", "7", "2", "3", "4" ]
[ "nonn", "new" ]
14
1
1
[ "A385182", "A385183" ]
null
Clark Kimberling, Jun 23 2025
2025-07-10T00:26:36
oeisdata/seq/A385/A385183.seq
e6cd50594103b7fc6ca4f5c49e3a6ed3
A385184
The w sequence in quartets (1,u,v,w); see A385182.
[ "1", "2", "3", "4", "1", "5", "2", "6", "7", "3", "8", "1", "4", "9", "10", "5", "2", "11", "6", "12", "3", "13", "7", "1", "14", "4", "8", "15", "2", "16", "9", "5", "17", "10", "18", "6", "3", "19", "11", "1", "20", "7", "12", "4", "21", "22", "13", "8", "2", "23", "5", "14", "24", "9", "25", "15", "3", "6", "26", "10", "1", "16", "27", "28", "17", "11", "7", "4", "29", "18", "2", "30", "12", "8", "31" ]
[ "nonn", "new" ]
11
1
2
[ "A385182", "A385184" ]
null
Clark Kimberling, Jun 26 2025
2025-07-10T00:27:32
oeisdata/seq/A385/A385184.seq
2d29189c1ea7e866f892b8e0d5a9dc08
A385186
Numbers y such that there exists an integer 0 < x < y such that sigma(x)^x * sigma(y)^y = (x+y)^(x+y).
[ "284", "1210", "2924", "5564", "6368", "10856", "14595", "18416", "76084", "66992", "71145", "87633", "88730", "124155", "139815", "123152", "153176", "168730", "176336", "180848", "203432", "202444", "365084", "389924", "430402", "399592", "455344", "486178", "514736", "525915", "669688", "686072" ]
[ "nonn", "hard" ]
9
1
1
[ "A000203", "A002046", "A383932", "A385186" ]
null
S. I. Dimitrov, Jun 20 2025
2025-06-26T19:28:49
oeisdata/seq/A385/A385186.seq
67617c8b26d4413f205327866de362d0
A385187
Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A002378(n) and its long leg and hypotenuse are consecutive natural numbers.
[ "1", "6", "330", "3036", "14820", "51330", "142926", "341880", "731016", "1433790", "2625810", "4547796", "7519980", "11957946", "18389910", "27475440", "40025616", "57024630", "79652826", "109311180", "147647220", "196582386", "258340830", "335479656", "430920600", "547983150", "690419106", "862448580", "1068797436", "1314736170", "1606120230" ]
[ "nonn", "easy" ]
6
1
2
[ "A002378", "A142463", "A385022", "A385187" ]
null
Miguel-Ángel Pérez García-Ortega, Jun 20 2025
2025-07-02T16:42:00
oeisdata/seq/A385/A385187.seq
089d5398972d9bf5d621600b496f2e1e
A385188
Primes p == 3 (mod 4) such that the multiplicative order of 2+-i modulo p in Gaussian integers (A385165) is not divisible by 2 or 3.
[ "599", "691", "1291", "1451", "2411", "3851", "4919", "5051", "5479", "5531", "5879", "6599", "7079", "7691", "8011", "8039", "11491", "13291", "14011", "15091", "15971", "16651", "17359", "18731", "19211", "19531", "20731", "22651", "23971", "24611", "25639", "25679", "26251", "32051", "32359", "32531", "32771", "32971", "35879", "37039", "37571", "38011", "38371" ]
[ "nonn", "easy" ]
14
1
1
[ "A122869", "A385165", "A385167", "A385168", "A385169", "A385179", "A385180", "A385188", "A385191", "A385219" ]
null
Jianing Song, Jun 20 2025
2025-06-22T21:32:26
oeisdata/seq/A385/A385188.seq
f7a4300bcbf916f3f40a72b6d7b2a622
A385189
Intersection of A055932 and A002378.
[ "2", "6", "12", "30", "72", "90", "210", "240", "420", "600", "1260", "6480", "15750", "50400", "147840", "194040", "291060", "510510", "2942940", "4324320", "5762400", "9147600", "19136250", "96049800", "153153000", "15178363200", "37822664880", "401392571580" ]
[ "nonn", "fini", "full" ]
34
1
1
[ "A002110", "A002378", "A007947", "A055932", "A385189" ]
null
Ken Clements, Jun 20 2025
2025-06-27T23:34:45
oeisdata/seq/A385/A385189.seq
b3521a084d1bd77ff58c8e3527a41c7c
A385190
Primes p == 3 (mod 4), p > 3 such that 1+-i are 24th powers modulo p.
[ "31", "127", "191", "223", "383", "479", "863", "1151", "1439", "1471", "1823", "2111", "2143", "2207", "2399", "2591", "2687", "2879", "3167", "3359", "3391", "4127", "4703", "4799", "5087", "5279", "5471", "5503", "6047", "6079", "6143", "6271", "6719", "6911", "7103", "7487", "7583", "8191", "8287", "8447", "8543", "8831", "8863", "9311", "9439", "9631", "9791", "9887" ]
[ "nonn", "easy" ]
12
1
1
[ "A002145", "A385163", "A385190", "A385191" ]
null
Jianing Song, Jun 20 2025
2025-06-21T00:45:53
oeisdata/seq/A385/A385190.seq
11c4b386d8353c8d1ef5aad26c2531ae
A385191
Primes p == 3 (mod 4), p > 3 such that 2+-i are 24th powers modulo p.
[ "599", "691", "1039", "1291", "1451", "1759", "2411", "2879", "3079", "3491", "3851", "4519", "4639", "4919", "5051", "5479", "5519", "5531", "5639", "5879", "6011", "6079", "6599", "6719", "7079", "7691", "8011", "8039", "8171", "8731", "9439", "9839", "10799", "11159", "11239", "11411", "11491", "12239", "12799", "13291", "13679", "13759", "13879", "14011", "14639" ]
[ "nonn", "easy" ]
11
1
1
[ "A002145", "A122869", "A385165", "A385188", "A385190", "A385191" ]
null
Jianing Song, Jun 20 2025
2025-06-21T00:45:49
oeisdata/seq/A385/A385191.seq
4a2b46ab9a2dae408c958097cb1294e7
A385192
Primes p such that multiplicative order of 5 modulo p is odd.
[ "2", "11", "19", "31", "59", "71", "79", "101", "109", "131", "139", "149", "151", "179", "181", "191", "199", "211", "239", "251", "269", "271", "311", "331", "359", "379", "389", "401", "409", "419", "431", "439", "461", "479", "491", "499", "541", "569", "571", "599", "619", "631", "659", "691", "719", "739", "751", "811", "829", "839", "859", "911", "919", "941", "971", "991" ]
[ "nonn", "easy" ]
23
1
1
[ "A014663", "A040105", "A045468", "A122869", "A163183", "A385192", "A385193", "A385220", "A385221", "A385223", "A385224", "A385225" ]
null
Jianing Song, Jun 20 2025
2025-06-28T12:53:24
oeisdata/seq/A385/A385192.seq
5544c127c0e3adb0960b37dd7ae2502c
A385193
Odd multiplicative orders of 5 modulo primes.
[ "1", "5", "9", "3", "29", "5", "39", "25", "27", "65", "69", "37", "75", "89", "15", "19", "33", "35", "119", "25", "67", "27", "155", "165", "179", "21", "97", "25", "17", "209", "215", "219", "115", "239", "245", "249", "135", "71", "285", "299", "309", "35", "329", "115", "359", "123", "375", "405", "9", "419", "429", "455", "459", "235", "485", "495", "509", "255", "515", "173", "525", "265", "267", "109", "575", "45" ]
[ "nonn", "easy" ]
26
1
2
[ "A139686", "A211241", "A385192", "A385193", "A385226", "A385227", "A385228", "A385229", "A385230", "A385231" ]
null
Jianing Song, Jun 20 2025
2025-06-28T17:08:45
oeisdata/seq/A385/A385193.seq
5ef523d246a2477be6561ac25af07c66
A385194
Minimum number of steps to reach n by repeated doubling and/or digit reversal starting from 1, or -1 if n cannot be reached.
[ "0", "1", "-1", "2", "37", "-1", "29", "3", "-1", "38", "-1", "-1", "33", "30", "-1", "4", "14", "-1", "25", "39", "-1", "-1", "6", "-1", "35", "34", "-1", "31", "9", "-1", "33", "5", "-1", "12", "28", "-1", "17", "25", "-1", "40", "30", "-1", "13", "-1", "-1", "7", "19", "-1", "18", "36", "-1", "35", "28", "-1", "-1", "32", "-1", "10", "24", "-1", "5", "34", "-1", "6", "32", "-1", "27", "13" ]
[ "sign", "base" ]
11
1
4
[ "A004086", "A385194" ]
null
David Radcliffe, Jun 20 2025
2025-06-22T03:32:19
oeisdata/seq/A385/A385194.seq
808585930f65c8b0c884ece1fe0d1143
A385195
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is either 1 or 2.
[ "1", "2", "2", "3", "4", "4", "6", "7", "8", "8", "10", "6", "12", "12", "8", "15", "16", "16", "18", "12", "12", "20", "22", "14", "24", "24", "26", "18", "28", "16", "30", "31", "20", "32", "24", "24", "36", "36", "24", "28", "40", "24", "42", "30", "32", "44", "46", "30", "48", "48", "32", "36", "52", "52", "40", "42", "36", "56", "58", "24", "60", "60", "48", "63", "48", "40", "66", "48", "44" ]
[ "nonn", "easy", "mult" ]
11
1
2
[ "A047994", "A065463", "A077610", "A126246", "A138191", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058", "A385195", "A385196", "A385197", "A385198", "A385199" ]
null
Amiram Eldar, Jun 21 2025
2025-06-22T16:33:52
oeisdata/seq/A385/A385195.seq
88f62a5b32fa0dd60a93c9a7ab368ab4
A385196
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a prime number.
[ "0", "1", "1", "0", "1", "3", "1", "0", "0", "5", "1", "3", "1", "7", "6", "0", "1", "8", "1", "3", "8", "11", "1", "7", "0", "13", "0", "3", "1", "14", "1", "0", "12", "17", "10", "0", "1", "19", "14", "7", "1", "20", "1", "3", "8", "23", "1", "15", "0", "24", "18", "3", "1", "26", "14", "7", "20", "29", "1", "18", "1", "31", "8", "0", "16", "32", "1", "3", "24", "34", "1", "0", "1", "37", "24", "3", "16", "38" ]
[ "nonn", "easy" ]
10
1
6
[ "A010051", "A047994", "A065463", "A077610", "A117494", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058", "A385195", "A385196", "A385197", "A385198", "A385199" ]
null
Amiram Eldar, Jun 21 2025
2025-06-23T02:46:10
oeisdata/seq/A385/A385196.seq
4a4b44810b20bf4fde2b2ccf5ed0f0dc
A385197
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a noncomposite number.
[ "1", "2", "3", "3", "5", "5", "7", "7", "8", "9", "11", "9", "13", "13", "14", "15", "17", "16", "19", "15", "20", "21", "23", "21", "24", "25", "26", "21", "29", "22", "31", "31", "32", "33", "34", "24", "37", "37", "38", "35", "41", "32", "43", "33", "40", "45", "47", "45", "48", "48", "50", "39", "53", "52", "54", "49", "56", "57", "59", "42", "61", "61", "56", "63", "64", "52", "67", "51" ]
[ "nonn", "easy" ]
7
1
2
[ "A047994", "A065463", "A077610", "A080339", "A349338", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058", "A385195", "A385196", "A385197", "A385198", "A385199" ]
null
Amiram Eldar, Jun 21 2025
2025-06-22T16:33:43
oeisdata/seq/A385/A385197.seq
264f1bf501ea7a0d74ccc6819fb8d937
A385198
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a prime power (A246655).
[ "0", "1", "1", "1", "1", "3", "1", "1", "1", "5", "1", "5", "1", "7", "6", "1", "1", "9", "1", "7", "8", "11", "1", "9", "1", "13", "1", "9", "1", "14", "1", "1", "12", "17", "10", "11", "1", "19", "14", "11", "1", "20", "1", "13", "12", "23", "1", "17", "1", "25", "18", "15", "1", "27", "14", "13", "20", "29", "1", "26", "1", "31", "14", "1", "16", "32", "1", "19", "24", "34", "1", "15", "1", "37", "26", "21" ]
[ "nonn", "easy" ]
7
1
6
[ "A047994", "A065463", "A069513", "A077610", "A116512", "A246655", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058", "A385195", "A385196", "A385197", "A385198", "A385199" ]
null
Amiram Eldar, Jun 21 2025
2025-06-22T16:33:37
oeisdata/seq/A385/A385198.seq
305e524afe611a8d246461437998da5c
A385199
The number of integers k from 1 to n such that the greatest divisor of k that is either 1 or a prime power (A000961).
[ "1", "2", "3", "4", "5", "5", "7", "8", "9", "9", "11", "11", "13", "13", "14", "16", "17", "17", "19", "19", "20", "21", "23", "23", "25", "25", "27", "27", "29", "22", "31", "32", "32", "33", "34", "35", "37", "37", "38", "39", "41", "32", "43", "43", "44", "45", "47", "47", "49", "49", "50", "51", "53", "53", "54", "55", "56", "57", "59", "50", "61", "61", "62", "64", "64", "52", "67", "67" ]
[ "nonn", "easy" ]
7
1
2
[ "A000961", "A010055", "A047994", "A065463", "A077610", "A131233", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058", "A385195", "A385196", "A385197", "A385198", "A385199" ]
null
Amiram Eldar, Jun 21 2025
2025-06-22T16:33:31
oeisdata/seq/A385/A385199.seq
76a1769ffc9a575305a832a1efc35a06
A385200
The sum of the exponents e for the integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a prime power p^e.
[ "0", "1", "1", "2", "1", "3", "1", "3", "2", "5", "1", "7", "1", "7", "6", "4", "1", "10", "1", "11", "8", "11", "1", "13", "2", "13", "3", "15", "1", "14", "1", "5", "12", "17", "10", "22", "1", "19", "14", "19", "1", "20", "1", "23", "16", "23", "1", "23", "2", "26", "18", "27", "1", "29", "14", "25", "20", "29", "1", "34", "1", "31", "20", "6", "16", "32", "1", "35", "24", "34", "1", "38", "1", "37", "28" ]
[ "nonn", "easy" ]
8
1
4
[ "A047994", "A065463", "A077610", "A122410", "A246655", "A384047", "A385198", "A385200" ]
null
Amiram Eldar, Jun 21 2025
2025-06-22T16:33:21
oeisdata/seq/A385/A385200.seq
e691d2f99e57131c56222729898f420b
A385201
Palindromic primes indexed by palindromic primes.
[ "3", "5", "11", "131", "313", "94349", "1123211", "1212121", "1360631", "1422241", "3075703", "3293923", "3400043", "3447443", "9711179", "9852589", "100161001", "101171101", "108505801", "109111901", "13929592931", "14125852141", "14209390241", "14895559841", "14986568941", "15911711951", "16172327161", "16257475261", "16727672761" ]
[ "nonn", "base", "easy" ]
8
1
1
[ "A000040", "A002113", "A002385", "A385201" ]
null
Alexander Yutkin, Jun 21 2025
2025-06-27T16:11:57
oeisdata/seq/A385/A385201.seq
178dc3d09e45eb4e74ad8732c7bc5732
A385202
Irregular triangle read by rows: let S be an ordered set of nondivisors of n such that a and b belong to S if a + b = n. T(n,k) is the k-th member of S. If S is empty, T(n,k) = 0.
[ "0", "0", "0", "0", "2", "3", "0", "2", "3", "4", "5", "3", "5", "2", "4", "5", "7", "3", "4", "6", "7", "2", "3", "4", "5", "6", "7", "8", "9", "5", "7", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "3", "4", "5", "6", "8", "9", "10", "11", "2", "4", "6", "7", "8", "9", "11", "13", "3", "5", "6", "7", "9", "10", "11", "13", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "4", "5", "7", "8", "10", "11", "13", "14" ]
[ "nonn", "tabf" ]
6
1
5
[ "A086369", "A385202" ]
null
Miles Englezou, Jun 21 2025
2025-06-26T23:00:02
oeisdata/seq/A385/A385202.seq
c404da1ad89dc4a69452d1bb074fba3a
A385203
G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^2 )^(1/5).
[ "1", "5", "0", "-125", "625", "5625", "-87500", "0", "9140625", "-60156250", "-653125000", "11654296875", "0", "-1470068359375", "10353515625000", "118916992187500", "-2225148925781250", "0", "302784667968750000", "-2199076690673828125", "-25952287445068359375", "497460246276855468750", "0" ]
[ "sign" ]
9
0
2
[ "A078534", "A385203", "A385204", "A385205" ]
null
Seiichi Manyama, Jun 21 2025
2025-06-21T11:50:32
oeisdata/seq/A385/A385203.seq
bbe63a215381f310a5cfe2699f15a85f
A385204
G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^3 )^(1/5).
[ "1", "5", "25", "0", "-1250", "-6875", "65625", "1062500", "0", "-116796875", "-782031250", "8609375000", "155390625000", "0", "-19950927734375", "-141498046875000", "1635108642578125", "30759411621093750", "0", "-4223049316406250000", "-30787073669433593750", "364567847442626953125" ]
[ "sign" ]
11
0
2
[ "A078534", "A385203", "A385204", "A385205" ]
null
Seiichi Manyama, Jun 21 2025
2025-06-22T00:16:27
oeisdata/seq/A385/A385204.seq
b016ee7223d49e79942548bc5324fd80
A385205
G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^4 )^(1/5).
[ "1", "5", "50", "500", "4375", "27500", "0", "-3562500", "-70078125", "-876562500", "-6926562500", "0", "1189169921875", "25690820312500", "346441406250000", "2911880859375000", "0", "-550017993164062500", "-12339622131347656250", "-171953389892578125000", "-1487552714691162109375", "0" ]
[ "sign" ]
15
0
2
[ "A078534", "A182122", "A299958", "A376636", "A385203", "A385204", "A385205", "A385207" ]
null
Seiichi Manyama, Jun 21 2025
2025-06-21T11:49:31
oeisdata/seq/A385/A385205.seq
eb30a0ee1f49bcddcfd18839c90baf8a
A385206
G.f. A(x) satisfies A(x) = ( 1 + 49*x*A(x) )^(1/7).
[ "1", "7", "-98", "1715", "-28812", "369754", "0", "-234003861", "11187831655", "-379208609780", "10505577339166", "-237021026782414", "3747904201751920", "0", "-3136632447485449416", "165539296779239527515", "-6087083256734433868530", "180571542422445599417377", "-4318405727843353425012650" ]
[ "sign" ]
13
0
2
[ "A182122", "A385206", "A385207", "A385208" ]
null
Seiichi Manyama, Jun 21 2025
2025-06-21T11:49:23
oeisdata/seq/A385/A385206.seq
c9b6118bfabafaaec778a4d37c9224f8
A385207
G.f. A(x) satisfies A(x) = ( 1 + 49*x*A(x)^6 )^(1/7).
[ "1", "7", "147", "3430", "79233", "1714314", "32471124", "450360372", "0", "-313409171166", "-15459345780879", "-537166232508360", "-15185812043764453", "-348420909370148580", "-5588125164812112720", "0", "4783756561471246040577", "254794190560328322173970", "9445124186699596552669050" ]
[ "sign" ]
13
0
2
[ "A182122", "A376636", "A385205", "A385206", "A385207", "A385208" ]
null
Seiichi Manyama, Jun 21 2025
2025-06-21T11:44:12
oeisdata/seq/A385/A385207.seq
9b219371d210d25c6538c237942ca35b
A385208
G.f. A(x) satisfies A(x) = ( 1 + 49*x*A(x)^8 )^(1/7).
[ "1", "7", "245", "11319", "593047", "33429123", "1977326743", "121034349975", "7601257418678", "487008549508481", "31705597390195820", "2091361378163375955", "139468121325692304390", "9387480337647754305649", "636914947847207765431080", "43512658997082838985965655", "2990750175103769856729417627" ]
[ "nonn" ]
11
0
2
[ "A078531", "A078532", "A078533", "A078534", "A078535", "A385206", "A385207", "A385208" ]
null
Seiichi Manyama, Jun 21 2025
2025-06-21T11:50:21
oeisdata/seq/A385/A385208.seq
50b49e250f1d85a9b39b5f07be320103
A385209
Least k such that A086369(k) = n.
[ "1", "2", "3", "4", "9", "6", "15", "16", "81", "12", "45", "64", "729", "24", "105", "36", "225", "48", "405", "1024", "59049", "60", "315", "4096", "531441", "192", "3645", "144", "2025", "120", "945", "65536", "43046721", "180", "1575", "262144", "387420489", "240", "2835", "576", "18225", "3072", "295245", "4194304", "31381059609", "360", "3465", "1296" ]
[ "nonn" ]
22
1
2
[ "A086369", "A385202", "A385209" ]
null
Miles Englezou, Jun 21 2025
2025-06-30T07:43:23
oeisdata/seq/A385/A385209.seq
df9ab13621c16a244bab05dccea2a1a5
A385210
Number of integers k such that prime(n) + primorial(k) is prime.
[ "1", "1", "2", "2", "3", "3", "5", "2", "5", "5", "4", "5", "8", "3", "5", "4", "7", "7", "8", "7", "8", "8", "7", "6", "5", "11", "8", "9", "8", "3", "6", "6", "5", "3", "7", "10", "10", "7", "8", "9", "5", "6", "7", "8", "6", "8", "6", "12", "5", "11", "10", "14", "8", "7", "8", "8", "7", "6", "6", "9", "9", "11", "8", "10", "10", "9", "12", "8", "8", "8", "6", "9", "11", "11", "7", "13", "5", "11", "5", "9", "10", "9", "9", "7", "8" ]
[ "nonn" ]
21
1
3
[ "A000040", "A002110", "A385210" ]
null
Daniel D Gibson, Jun 21 2025
2025-06-22T09:39:38
oeisdata/seq/A385/A385210.seq
f8d8c074632c158c740e2fb2065c36e6
A385211
Number of minimum dominating sets in the n-Pasechnik graph.
[ "27", "12789", "43560", "14994" ]
[ "nonn", "more" ]
4
1
1
null
null
Eric W. Weisstein, Jun 21 2025
2025-06-21T11:49:08
oeisdata/seq/A385/A385211.seq
986e8e5c8d48fcd1fc84475929b48169
A385212
a(n) = n^(mu(n)^2), where mu is the Möbius function (A008683).
[ "1", "2", "3", "1", "5", "6", "7", "1", "1", "10", "11", "1", "13", "14", "15", "1", "17", "1", "19", "1", "21", "22", "23", "1", "1", "26", "1", "1", "29", "30", "31", "1", "33", "34", "35", "1", "37", "38", "39", "1", "41", "42", "43", "1", "1", "46", "47", "1", "1", "1", "51", "1", "53", "1", "55", "1", "57", "58", "59", "1", "61", "62", "1", "1", "65", "66", "67", "1", "69", "70", "71", "1", "73", "74", "1", "1", "77", "78", "79", "1", "1", "82", "83", "1", "85", "86", "87", "1", "89", "1", "91", "1", "93", "94", "95", "1", "97", "1", "1", "1" ]
[ "nonn", "changed" ]
20
1
2
[ "A008683", "A008966", "A013661", "A055615", "A107078", "A344465", "A385212" ]
null
Wesley Ivan Hurt, Jun 21 2025
2025-07-05T11:50:49
oeisdata/seq/A385/A385212.seq
8335b53e9489d52cfdcbdbcf81ec469a
A385213
Number of maximal runs of consecutive parts increasing by 1 in the prime indices of n (with multiplicity).
[ "0", "1", "1", "2", "1", "1", "1", "3", "2", "2", "1", "2", "1", "2", "1", "4", "1", "2", "1", "3", "2", "2", "1", "3", "2", "2", "3", "3", "1", "1", "1", "5", "2", "2", "1", "3", "1", "2", "2", "4", "1", "2", "1", "3", "2", "2", "1", "4", "2", "3", "2", "3", "1", "3", "2", "4", "2", "2", "1", "2", "1", "2", "3", "6", "2", "2", "1", "3", "2", "2", "1", "4", "1", "2", "2", "3", "1", "2", "1", "5", "4", "2", "1", "3", "2", "2", "2" ]
[ "nonn" ]
6
1
4
[ "A000079", "A002110", "A034839", "A048767", "A055396", "A056239", "A061395", "A069010", "A112798", "A116674", "A130091", "A300820", "A351202", "A356606", "A382525", "A384877", "A384878", "A384890", "A384893", "A384906", "A385213" ]
null
Gus Wiseman, Jun 22 2025
2025-06-22T14:37:42
oeisdata/seq/A385/A385213.seq
a059467774740527e27aa5f296b132b4
A385214
Number of subsets of {1..n} without all equal lengths of maximal runs of consecutive elements increasing by 1.
[ "0", "0", "0", "0", "2", "8", "25", "66", "159", "361", "791", "1688", "3539", "7328", "15040", "30669", "62246", "125896", "253975", "511357", "1028052" ]
[ "nonn", "more" ]
5
0
5
[ "A010027", "A034839", "A044813", "A049988", "A116674", "A164707", "A164708", "A164710", "A243815", "A268193", "A325325", "A329738", "A329739", "A383013", "A384175", "A384176", "A384177", "A384879", "A384884", "A384885", "A384886", "A384887", "A384888", "A384889", "A384891", "A384892", "A384893", "A384904", "A384905", "A385214" ]
null
Gus Wiseman, Jun 25 2025
2025-06-25T18:04:35
oeisdata/seq/A385/A385214.seq
d17fdc5f78aad19aa98e9f9e752d19a7
A385215
Number of maximal sparse submultisets of the prime indices of n, where a multiset is sparse iff 1 is not a first difference.
[ "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1" ]
[ "nonn" ]
8
1
6
[ "A000045", "A000071", "A001629", "A034839", "A116674", "A166469", "A202064", "A245564", "A268193", "A316476", "A319630", "A374356", "A384883", "A384884", "A384887", "A384890", "A384893", "A384905", "A385215", "A385216" ]
null
Gus Wiseman, Jul 03 2025
2025-07-03T10:08:31
oeisdata/seq/A385/A385215.seq
2fcf500f69579588987e5dc41c2cfe5b
A385216
Greatest Heinz number of a sparse submultiset of the prime indices of n, where a multiset is sparse iff 1 is not a first difference.
[ "1", "2", "3", "4", "5", "3", "7", "8", "9", "10", "11", "4", "13", "14", "5", "16", "17", "9", "19", "20", "21", "22", "23", "8", "25", "26", "27", "28", "29", "10", "31", "32", "33", "34", "7", "9", "37", "38", "39", "40", "41", "21", "43", "44", "9", "46", "47", "16", "49", "50", "51", "52", "53", "27", "55", "56", "57", "58", "59", "20", "61", "62", "63", "64", "65", "33", "67", "68", "69" ]
[ "nonn", "new" ]
5
1
2
[ "A000005", "A000720", "A001221", "A001222", "A005117", "A008284", "A051903", "A051904", "A055396", "A056239", "A061395", "A091602", "A104210", "A112798", "A122111", "A130091", "A166469", "A212166", "A239964", "A240312", "A245564", "A268193", "A316476", "A319630", "A374356", "A381542", "A384883", "A385215", "A385216" ]
null
Gus Wiseman, Jul 05 2025
2025-07-06T17:49:16
oeisdata/seq/A385/A385216.seq
1a53b8419b98221e12f78a19a9d82966
A385217
Odd multiplicative orders of 2+-i modulo primes p == 3 (mod 4).
[ "13695", "40755", "7475", "19895", "43995", "117855", "138075", "13185", "69445", "87725", "308505", "220665", "567645", "80735", "1103355", "1321125", "1386945", "507795", "1594005", "130995", "205975", "2051325", "2092035", "2216565", "2703975", "1368315", "2750685", "504095", "3039345", "212605", "3342405", "125081", "1274665", "3991725", "152205", "4279275" ]
[ "nonn", "easy" ]
11
1
1
[ "A385165", "A385169", "A385217", "A385218", "A385219" ]
null
Jianing Song, Jun 22 2025
2025-06-23T10:24:43
oeisdata/seq/A385/A385217.seq
88fe48cbe370f831d3110866e60dbbb0
A385218
Multiplicative orders of 2+-i modulo p == 3 (mod 4) that are congruent to 2 modulo 4.
[ "30", "4290", "3710", "3150", "20090", "164430", "21114", "22490", "59514", "43494", "244650", "65110", "819930", "932190", "1011030", "1266750", "1405410", "533830", "1864590", "135470", "2266530", "79002", "946970", "3863190", "1039890", "4952850", "170178", "566202", "6277530", "1324930", "3091690", "9397290", "214314", "5054610", "3467950", "3511090" ]
[ "nonn", "easy" ]
13
1
1
[ "A385165", "A385179", "A385217", "A385218", "A385219" ]
null
Jianing Song, Jun 22 2025
2025-06-23T10:25:35
oeisdata/seq/A385/A385218.seq
f11d8e6365d0f45974a4d7b2b98ee293
A385219
Multiplicative orders of 2+-i modulo p == 3 (mod 4) that are not divisible by 2 or 3.
[ "7475", "19895", "69445", "87725", "80735", "205975", "504095", "212605", "125081", "1274665", "720055", "181445", "1044005", "492929", "891335", "1346365", "5501795", "7360445", "8179505", "9489095", "10628035", "3850775", "3138905", "14618765", "15377605", "34181", "17907265", "21377825", "23942035", "5047511", "13694965", "6868865", "28713125" ]
[ "nonn", "easy" ]
13
1
1
[ "A385165", "A385188", "A385217", "A385218", "A385219" ]
null
Jianing Song, Jun 22 2025
2025-06-23T10:25:31
oeisdata/seq/A385/A385219.seq
6a73da7ed9f826a6f42c5fe1cdc3f956
A385220
Primes p such that multiplicative order of 3 modulo p is odd.
[ "2", "11", "13", "23", "47", "59", "71", "83", "107", "109", "131", "167", "179", "181", "191", "227", "229", "239", "251", "263", "277", "311", "313", "347", "359", "383", "419", "421", "431", "433", "443", "467", "479", "491", "503", "541", "563", "587", "599", "601", "647", "659", "683", "709", "719", "733", "743", "757", "827", "829", "839", "863", "887", "911", "947", "971", "983" ]
[ "nonn", "easy" ]
22
1
1
[ "A014663", "A040101", "A045317", "A068231", "A097933", "A163183", "A301916", "A385192", "A385220", "A385221", "A385223", "A385224", "A385225", "A385226" ]
null
Jianing Song, Jun 22 2025
2025-06-28T12:53:34
oeisdata/seq/A385/A385220.seq
b7325e5ea1877e28432c239911ab386f
A385221
Primes p such that multiplicative order of 4 modulo p is odd.
[ "3", "7", "11", "19", "23", "31", "43", "47", "59", "67", "71", "73", "79", "83", "89", "103", "107", "127", "131", "139", "151", "163", "167", "179", "191", "199", "211", "223", "227", "233", "239", "251", "263", "271", "281", "283", "307", "311", "331", "337", "347", "359", "367", "379", "383", "419", "431", "439", "443", "463", "467", "479", "487", "491", "499", "503", "523", "547", "563" ]
[ "nonn", "easy" ]
19
1
1
[ "A002145", "A014663", "A163183", "A385192", "A385220", "A385221", "A385223", "A385224", "A385225", "A385227" ]
null
Jianing Song, Jun 22 2025
2025-06-28T12:53:42
oeisdata/seq/A385/A385221.seq
88fbc8aef38dd59f5d1f4a4f418aec4c
A385222
a(n) is the multiplicative order of -10 modulo prime(n); a(1) = a(3) = 0 for completion.
[ "0", "2", "0", "3", "1", "3", "16", "9", "11", "28", "30", "6", "10", "42", "23", "26", "29", "60", "66", "70", "8", "26", "82", "44", "96", "4", "17", "106", "108", "112", "21", "65", "8", "23", "148", "150", "39", "162", "83", "86", "89", "180", "190", "192", "49", "198", "15", "111", "226", "228", "232", "14", "15", "25", "256", "131", "268", "10", "138", "28" ]
[ "nonn", "easy", "changed" ]
18
1
2
[ "A002371", "A007348", "A014664", "A062117", "A082654", "A211241", "A211242", "A211243", "A211244", "A211245", "A337878", "A380482", "A380531", "A380532", "A380533", "A380540", "A380541", "A380542", "A385222" ]
null
Jianing Song, Jun 27 2025
2025-07-07T10:44:10
oeisdata/seq/A385/A385222.seq
868e0da557bb5ce66b1925e06c0ca3ca
A385223
Primes p such that multiplicative order of -3 modulo p is odd.
[ "2", "7", "19", "31", "37", "43", "61", "67", "79", "103", "127", "139", "151", "157", "163", "199", "211", "223", "271", "283", "307", "331", "349", "367", "373", "379", "397", "439", "463", "487", "499", "523", "547", "571", "607", "613", "619", "631", "643", "661", "691", "727", "739", "751", "787", "811", "823", "853", "859", "877", "883", "907", "919", "937", "967", "991", "997" ]
[ "nonn", "easy" ]
21
1
1
[ "A002476", "A014663", "A068229", "A163183", "A385192", "A385220", "A385221", "A385223", "A385224", "A385225", "A385229" ]
null
Jianing Song, Jun 22 2025
2025-06-28T11:15:26
oeisdata/seq/A385/A385223.seq
b620aacf1ee191e8397502adb3e96e7c
A385224
Primes p such that multiplicative order of -4 modulo p is odd.
[ "5", "13", "29", "37", "41", "53", "61", "101", "109", "113", "137", "149", "157", "173", "181", "197", "229", "269", "277", "293", "313", "317", "349", "373", "389", "397", "409", "421", "457", "461", "509", "521", "541", "557", "569", "593", "613", "653", "661", "677", "701", "709", "733", "757", "761", "773", "797", "809", "821", "829", "853", "857", "877", "941", "953", "997" ]
[ "nonn", "easy" ]
20
1
1
[ "A002144", "A007521", "A014663", "A133204", "A163183", "A385192", "A385220", "A385221", "A385223", "A385224", "A385225", "A385230" ]
null
Jianing Song, Jun 22 2025
2025-06-28T12:53:59
oeisdata/seq/A385/A385224.seq
a530e3d60df5338f15d9c43762c28523
A385225
Primes p such that multiplicative order of -5 modulo p is odd.
[ "2", "3", "7", "23", "29", "43", "47", "61", "67", "83", "103", "107", "127", "163", "167", "223", "227", "229", "263", "283", "307", "347", "349", "367", "383", "421", "443", "449", "463", "467", "487", "503", "509", "521", "523", "547", "563", "587", "607", "643", "647", "661", "683", "701", "709", "727", "743", "761", "787", "821", "823", "827", "863", "883", "887", "907", "947", "967", "983" ]
[ "nonn", "easy" ]
18
1
1
[ "A014663", "A122870", "A139513", "A163183", "A385192", "A385220", "A385221", "A385223", "A385224", "A385225", "A385231" ]
null
Jianing Song, Jun 22 2025
2025-06-28T15:33:33
oeisdata/seq/A385/A385225.seq
5a3d54e1869b52ada0af04d532704faa
A385226
Odd multiplicative orders of 3 modulo primes.
[ "1", "5", "3", "11", "23", "29", "35", "41", "53", "27", "65", "83", "89", "45", "95", "113", "57", "119", "125", "131", "69", "155", "39", "173", "179", "191", "209", "105", "43", "27", "221", "233", "239", "49", "251", "135", "281", "293", "299", "75", "323", "329", "31", "177", "359", "183", "371", "9", "413", "207", "419", "431", "443", "455", "473", "485", "491" ]
[ "nonn", "easy" ]
16
1
2
[ "A062117", "A139686", "A385193", "A385220", "A385226", "A385227", "A385228", "A385229", "A385230", "A385231" ]
null
Jianing Song, Jun 22 2025
2025-06-28T16:04:00
oeisdata/seq/A385/A385226.seq
cc91ed526538a0bdd7fc1fc3756a85b9
A385227
Odd multiplicative orders of 4 modulo primes.
[ "1", "3", "5", "9", "11", "5", "7", "23", "29", "33", "35", "9", "39", "41", "11", "51", "53", "7", "65", "69", "15", "81", "83", "89", "95", "99", "105", "37", "113", "29", "119", "25", "131", "135", "35", "47", "51", "155", "15", "21", "173", "179", "183", "189", "191", "209", "43", "73", "221", "231", "233", "239", "243", "245", "83", "251", "261", "273", "281", "57", "293" ]
[ "nonn", "easy" ]
16
1
2
[ "A082654", "A139686", "A385193", "A385221", "A385226", "A385227", "A385228", "A385229", "A385230", "A385231" ]
null
Jianing Song, Jun 22 2025
2025-06-28T16:03:50
oeisdata/seq/A385/A385227.seq
60d3ae882aecb1fcb7afda39708d6d47
A385228
Odd multiplicative orders of -2 modulo primes.
[ "1", "5", "9", "7", "29", "33", "41", "53", "65", "69", "81", "89", "105", "113", "25", "35", "47", "51", "15", "173", "189", "209", "221", "233", "245", "83", "261", "273", "281", "57", "293", "77", "309", "107", "329", "11", "115", "123", "393", "135", "413", "429", "441", "453", "473", "97", "509", "129", "131", "175", "545", "137", "561", "83", "585", "593", "149", "629", "641", "645", "653", "713", "725" ]
[ "nonn", "easy", "changed" ]
23
1
2
[ "A139686", "A163183", "A337878", "A385193", "A385226", "A385227", "A385228", "A385229", "A385230", "A385231" ]
null
Jianing Song, Jun 22 2025
2025-07-07T10:44:06
oeisdata/seq/A385/A385228.seq
83bbc9bc1a80a8cfaf97c0504472b684
A385229
Odd multiplicative orders of -3 modulo primes.
[ "1", "3", "9", "15", "9", "21", "5", "11", "39", "17", "63", "69", "25", "39", "81", "99", "105", "111", "15", "141", "17", "165", "87", "61", "93", "189", "99", "73", "231", "243", "83", "29", "7", "285", "303", "51", "103", "315", "107", "11", "345", "121", "369", "375", "131", "405", "411", "71", "429", "219", "63", "453", "153", "117", "161", "165", "83", "17", "519", "105", "531", "267", "543", "561", "117" ]
[ "nonn", "easy" ]
21
1
2
[ "A139686", "A380482", "A385193", "A385223", "A385226", "A385227", "A385228", "A385229", "A385230", "A385231" ]
null
Jianing Song, Jun 22 2025
2025-06-30T04:37:20
oeisdata/seq/A385/A385229.seq
2f13da276bab1e776b3e2a1a4574e5b1
A385230
Odd multiplicative orders of -4 modulo primes.
[ "1", "3", "7", "9", "5", "13", "15", "25", "9", "7", "17", "37", "13", "43", "45", "49", "19", "67", "23", "73", "39", "79", "87", "93", "97", "11", "51", "105", "19", "115", "127", "65", "135", "139", "71", "37", "153", "163", "165", "169", "175", "177", "61", "189", "95", "193", "199", "101", "205", "207", "213", "107", "219", "235", "17", "83", "23", "85", "265", "89", "91", "277", "279", "141", "59", "75" ]
[ "nonn", "easy" ]
21
1
2
[ "A139686", "A380531", "A385193", "A385224", "A385226", "A385227", "A385228", "A385229", "A385230", "A385231" ]
null
Jianing Song, Jun 22 2025
2025-06-30T04:38:06
oeisdata/seq/A385/A385230.seq
87bf9c0d9743ca8baca52117d6035bb9