Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
2
sequence_id
stringlengths
7
7
sequence_name
stringlengths
4
573
sequence
listlengths
1
348
keywords
listlengths
1
8
score
int64
1
2.35k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
listlengths
1
128
⌀
former_ids
listlengths
1
3
⌀
author
stringlengths
7
231
⌀
timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-07-19 00:40:46
filename
stringlengths
29
29
hash
stringlengths
32
32
A383117
Indices of record high-water marks of the sequence abs((cos p)^p) where p is the numerator of the n-th convergent to Pi (A002485), starting from n = 1.
[ "1", "2", "3", "5", "13", "17", "18", "19", "20", "22", "26", "28", "30", "32", "33", "34", "38", "39", "40", "43", "44", "46", "48", "49", "50", "52", "53", "55", "59", "62", "65", "67", "70", "71", "72", "73", "75", "76", "77", "78", "80", "81", "83", "86", "88", "90", "91", "95", "97", "98", "100", "102", "103", "105", "106", "107", "109", "110", "111", "112", "114", "117", "119", "122", "123", "124", "125", "127", "129" ]
[ "nonn" ]
52
1
2
[ "A002485", "A382564", "A383117" ]
null
Jwalin Bhatt, May 01 2025
2025-05-07T08:26:20
oeisdata/seq/A383/A383117.seq
d69a8cc8a1fdf1fce01dffef2b29786d
A383118
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(3*k,k).
[ "1", "2", "10", "47", "238", "1232", "6499", "34715", "187198", "1016840", "5555560", "30497150", "168073195", "929348396", "5153362231", "28646281502", "159579236014", "890644144580", "4979200476088", "27878225498030", "156298588113088", "877350590047496", "4930273302851830", "27733610884176338" ]
[ "nonn" ]
15
0
2
[ "A002426", "A005809", "A127897", "A188686", "A346628", "A383118", "A383119" ]
null
Ilya Gutkovskiy, Apr 17 2025
2025-04-17T08:11:07
oeisdata/seq/A383/A383118.seq
3221067f4ce7e45e48b14e76d0010b18
A383119
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(4*k,k).
[ "1", "3", "21", "147", "1093", "8343", "64869", "510891", "4062277", "32539647", "262181601", "2122581123", "17252278789", "140695104943", "1150670390541", "9433965332127", "77512716483461", "638080242074447", "5261486780929209", "43450477494413751", "359308411992366513", "2974886601163646379", "24657831769475675253" ]
[ "nonn" ]
12
0
2
[ "A002426", "A005810", "A317133", "A346664", "A359643", "A383118", "A383119" ]
null
Ilya Gutkovskiy, Apr 17 2025
2025-04-17T08:11:03
oeisdata/seq/A383/A383119.seq
35e11a1a953f4f5afac5cdb12969e392
A383120
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k).
[ "1", "2", "11", "139", "2885", "82381", "2979565", "130203494", "6664589321", "390857822425", "25832193906761", "1899273577364197", "153741850998047053", "13585520026454056279", "1301210398133681268381", "134270617908678099820891", "14849785991790603714043921", "1752283118795349858851381297" ]
[ "nonn" ]
11
0
2
[ "A001850", "A014062", "A026375", "A188686", "A226391", "A359643", "A378327", "A383120", "A383121" ]
null
Ilya Gutkovskiy, Apr 17 2025
2025-04-17T14:54:49
oeisdata/seq/A383/A383120.seq
3a612b33972a5d14e2c94f2c29766aa5
A383121
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k).
[ "1", "0", "3", "47", "1093", "33029", "1236781", "55325416", "2879987209", "171061709417", "11418368571721", "846230146390001", "68949300160035373", "6126085419697733567", "589470974371501065845", "61068847238080533844679", "6777270943578364524130321", "802138434294752321142680145" ]
[ "nonn" ]
10
0
3
[ "A002426", "A349471", "A378409", "A383118", "A383119", "A383120", "A383121" ]
null
Ilya Gutkovskiy, Apr 17 2025
2025-04-17T14:54:44
oeisdata/seq/A383/A383121.seq
95674581b3c4b8280eb32d4ef345d863
A383122
a(n) is the smallest number that can be expressed as the sum of the smallest number of powers with different exponents greater than one in n different ways (for unitary bases, the smallest possible exponents are considered).
[ "1", "16", "17", "65", "80", "105", "139", "193", "329", "313", "336", "410", "477", "273", "553", "461", "436", "1219", "942", "10153", "1595", "1038", "722", "636", "1769", "1344", "2045", "2381", "1805", "2379", "3683", "2365", "1611", "3319", "3815", "4416", "4838", "4029", "3531", "5606", "5789", "4411", "4341", "5849", "7392", "1642", "4885", "8246", "3074", "5251", "5774", "3165", "2498", "12347", "9987", "5405", "8075", "11101", "2346", "6749" ]
[ "nonn" ]
11
1
2
[ "A351062", "A351063", "A351064", "A351065", "A351066", "A383122" ]
null
Alberto Zanoni, Apr 17 2025
2025-04-18T22:24:52
oeisdata/seq/A383/A383122.seq
4c6b3d590f7af720c84c53c84462e453
A383123
The Möbius transform of A382883.
[ "1", "-2", "-2", "2", "-2", "4", "-2", "0", "2", "4", "-2", "-3", "-2", "4", "4", "-1", "-2", "-3", "-2", "-3", "4", "4", "-2", "0", "2", "4", "0", "-3", "-2", "-8", "-2", "1", "4", "4", "4", "0", "-2", "4", "4", "0", "-2", "-8", "-2", "-3", "-3", "4", "-2", "1", "2", "-3", "4", "-3", "-2", "0", "4", "0", "4", "4", "-2", "5", "-2", "4", "-3", "-2", "4", "-8", "-2", "-3", "4", "-8", "-2", "1", "-2", "4" ]
[ "sign" ]
12
1
2
[ "A008683", "A382883", "A383123" ]
null
Peter Luschny, Apr 18 2025
2025-04-29T16:52:08
oeisdata/seq/A383/A383123.seq
df075887f01897ef0857a7d430a43195
A383124
a(n) = Sum_{d|n} A382883(d)*(n/d).
[ "1", "1", "2", "3", "4", "2", "6", "7", "7", "4", "10", "7", "12", "6", "8", "14", "16", "8", "18", "13", "12", "10", "22", "17", "21", "12", "22", "19", "28", "8", "30", "29", "20", "16", "24", "24", "36", "18", "24", "31", "40", "12", "42", "31", "29", "22", "46", "34", "43", "22", "32", "37", "52", "26", "40", "45", "36", "28", "58", "31", "60", "30", "43", "57", "48", "20", "66", "49", "44" ]
[ "nonn" ]
8
1
3
[ "A000010", "A047994", "A152958", "A382883", "A383104", "A383124" ]
null
Peter Luschny, Apr 17 2025
2025-04-29T16:52:03
oeisdata/seq/A383/A383124.seq
d16bfb2c5d73a3632ec81f502d739c22
A383125
Number of cyclic edge cuts in the n-web graph.
[ "8", "48", "2592", "113856", "3777664", "105202432", "2607968768", "59563461632", "1280762398720", "26305784328192", "521325843259392", "10041603365060608", "189005928050491392", "3490617343237881856", "63453465548367724544", "1138182144128359071744", "20185020166145139277824", "354486178810344080670720" ]
[ "nonn", "easy" ]
9
3
1
[ "A378311", "A383125" ]
null
Eric W. Weisstein, Apr 17 2025
2025-05-29T01:05:48
oeisdata/seq/A383/A383125.seq
fe1d67b48561627ccb013416106441de
A383126
Consecutive internal states of the linear congruential pseudo-random number generator (281*s + 28411) mod 134456 when started at 1.
[ "1", "28692", "23503", "44410", "3213", "124528", "62219", "32670", "65673", "62052", "120199", "55874", "132109", "41184", "37899", "56006", "34745", "110924", "4263", "16210", "11917", "15688", "134147", "76038", "16585", "117292", "45743", "108874", "100493", "31184", "51475", "106094", "126049", "86252", "63143", "23402" ]
[ "nonn", "look", "easy", "changed" ]
21
1
2
[ "A383126", "A383127", "A384431", "A385002", "A385003", "A385037", "A385039", "A385078" ]
null
Sean A. Irvine, Jun 17 2025
2025-07-06T18:23:15
oeisdata/seq/A383/A383126.seq
7996b79c1f889e2d741199fdbfde257d
A383127
Consecutive internal states of the linear congruential pseudo-random number generator (205*s + 29573) mod 139968 when started at 1.
[ "1", "29778", "115439", "39976", "106509", "28910", "77467", "93924", "108377", "131914", "58119", "46688", "82789", "65190", "96563", "89500", "41265", "90818", "31519", "52440", "2237", "68254", "24843", "83540", "79177", "24570", "27575", "83728", "117717", "87062", "101347", "90444", "94817", "11506", "8847", "23624", "113581" ]
[ "nonn", "easy", "changed" ]
17
1
2
[ "A383126", "A383127", "A384431", "A385002", "A385003", "A385037", "A385039", "A385078" ]
null
Sean A. Irvine, Jun 17 2025
2025-07-06T18:23:47
oeisdata/seq/A383/A383127.seq
f050e795ede357ab5ad3d8d47741076a
A383128
Consecutive internal states of the linear congruential pseudo-random number generator (321*s + 123) mod 10^5 when started at 1.
[ "1", "444", "42647", "89810", "29133", "51816", "33059", "12062", "72025", "20148", "67631", "9674", "5477", "58240", "95163", "47446", "30289", "22892", "48455", "54178", "91261", "94904", "64307", "42670", "97193", "99076", "3519", "29722", "40885", "24208", "70891", "56134", "19137", "43100", "35223", "6706", "52749", "32552" ]
[ "nonn", "look", "easy" ]
17
1
2
[ "A383126", "A383127", "A383128", "A384341" ]
null
Sean A. Irvine, Jun 17 2025
2025-06-18T11:23:34
oeisdata/seq/A383/A383128.seq
e608308ea909e529224a2b59a8bf63da
A383129
Consecutive internal states of the linear congruential pseudo-random number generator (421*s + 54773) mod 259200 when started at 1.
[ "1", "55194", "222647", "217960", "59133", "66566", "85459", "4212", "13625", "88498", "246831", "31424", "65077", "236190", "217163", "241996", "69489", "20042", "198055", "232728", "55661", "160054", "45507", "32420", "225193", "253026", "47519", "101872", "174885", "68558", "146491", "37884", "192737", "67450", "198423" ]
[ "nonn", "look", "easy" ]
20
1
2
[ "A383126", "A383127", "A383128", "A383129" ]
null
Sean A. Irvine, Jun 17 2025
2025-06-18T12:20:18
oeisdata/seq/A383/A383129.seq
2fe139285a10d77fc0f37c3162981a01
A383130
Coefficients of the linear terms in the continued fraction representation of the product logarithm.
[ "1", "1", "1", "5", "17", "133", "1927", "13582711", "92612482895", "10402118970990527", "59203666396198716260449", "83631044830029201279016528831", "1149522186344339904123210420373026673", "458029700061597358458976211208014885543904637441", "203695852839150317577316770934832249000714992664672874100151" ]
[ "nonn" ]
25
1
4
[ "A213236", "A383130" ]
null
Jacob DeMoss, Jun 17 2025
2025-06-25T00:36:58
oeisdata/seq/A383/A383130.seq
e67c3cfd22b92e2d8038f6db50a98ca2
A383131
a(n) is the number of iterations that n requires to reach 1 under the map x -> -x/2 if x is even, 3x + 1 if x is odd; a(n) = -1 if 1 is never reached.
[ "0", "3", "12", "2", "5", "5", "8", "5", "11", "11", "50", "14", "14", "14", "53", "4", "17", "17", "43", "7", "7", "7", "20", "7", "46", "46", "59", "10", "10", "10", "23", "7", "49", "49", "62", "13", "13", "13", "13", "13", "26", "26", "39", "52", "52", "52", "65", "16", "16", "16", "78", "16", "16", "16", "29", "16", "42", "42", "55", "55", "55", "55", "68", "6", "19", "19", "19", "19", "19" ]
[ "nonn" ]
17
1
2
[ "A006577", "A381055", "A383131" ]
null
Ya-Ping Lu, Apr 17 2025
2025-04-30T11:10:28
oeisdata/seq/A383/A383131.seq
ceeaee75d64bafd8a74e7fc1259259ab
A383132
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k) * n^k.
[ "1", "2", "33", "2701", "524993", "181752001", "97735073905", "75179269556672", "78240951854025217", "105806762566689176353", "180297512864534759056001", "377878889913778527874694227", "955217573424445946022789385537", "2865620569274978738097814056365899", "10064763360358683666070320479027168465" ]
[ "nonn" ]
7
0
2
[ "A084771", "A187021", "A331656", "A340971", "A383120", "A383132", "A383133" ]
null
Ilya Gutkovskiy, Apr 17 2025
2025-04-19T05:17:12
oeisdata/seq/A383/A383132.seq
2a678a605056ee9a7879db42442975a2
A383133
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k) * n^k.
[ "1", "0", "17", "1889", "412225", "151448249", "84430503361", "66535567456546", "70456680210155009", "96530372235620300465", "166169585125820280654001", "351113456811120647774884511", "893491183170443755035588745153", "2695374684029443253628238600963667", "9511442599320236554084097413617603681" ]
[ "nonn" ]
6
0
3
[ "A307885", "A331657", "A340972", "A383121", "A383132", "A383133" ]
null
Ilya Gutkovskiy, Apr 17 2025
2025-04-19T05:22:14
oeisdata/seq/A383/A383133.seq
8e3a628004ef40d50e39efb8e00d1701
A383134
Array read by ascending antidiagonals: A(n,k) is the length of the arithmetic progression of only primes having difference n and first term prime(k).
[ "2", "1", "1", "2", "3", "1", "1", "1", "2", "1", "2", "3", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "5", "1", "1", "1", "2", "1", "2", "3", "1", "3", "1", "2", "1", "1", "1", "1", "1", "2", "1", "4", "1", "1", "1", "1", "1", "2", "3", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "2", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "tabl" ]
12
1
1
[ "A000012", "A006512", "A040976", "A054977", "A088430", "A175191", "A206045", "A237453", "A383134" ]
null
Stefano Spezia, Apr 17 2025
2025-04-18T09:53:25
oeisdata/seq/A383/A383134.seq
1e8d5368aa7aae329ba46437ba15d244
A383135
a(n) = number of iterations that n requires to reach 1 under the x -> A380891(x) map, or -1 if it never does.
[ "0", "1", "2", "1", "3", "1", "5", "2", "3", "2", "3", "2", "4", "2", "4", "2", "6", "2", "4", "2", "6", "2", "13", "2", "13", "2", "8", "3", "8", "3", "10", "3", "10", "3", "3", "3", "10", "3", "5", "3", "10", "3", "5", "3", "5", "3", "6", "3", "5", "3", "5", "3", "17", "3", "5", "3", "5", "3", "17", "3", "3", "3", "3", "2", "12", "2", "3", "2", "5", "2", "5", "2", "12", "2", "3", "2", "7", "2", "3", "2", "7", "2", "7", "2" ]
[ "nonn" ]
24
1
3
[ "A006577", "A380891", "A381246", "A383135" ]
null
James C. McMahon and Vikram Prasad, Apr 17 2025
2025-05-05T16:44:05
oeisdata/seq/A383/A383135.seq
59252c3e1ec98181ac64121b46b326de
A383136
a(n) = Sum_{k=0..n} k^2 * 2^(n-k) * binomial(n,k).
[ "0", "1", "8", "45", "216", "945", "3888", "15309", "58320", "216513", "787320", "2814669", "9920232", "34543665", "119042784", "406552365", "1377495072", "4634696961", "15496819560", "51526925037", "170465015160", "561372288561", "1841022163728", "6014703091725", "19581781196016", "63546645708225", "205608702558168" ]
[ "nonn", "easy" ]
9
0
3
[ "A027471", "A383136", "A383137", "A383138", "A383139" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-17T12:27:58
oeisdata/seq/A383/A383136.seq
d1ac27a822d131860f2f01ee15488ea8
A383137
a(n) = Sum_{k=0..n} k^3 * 2^(n-k) * binomial(n,k).
[ "0", "1", "12", "87", "504", "2565", "11988", "52731", "221616", "898857", "3542940", "13640319", "51490728", "191141613", "699376356", "2527001955", "9030245472", "31955015889", "112093661484", "390132432423", "1348223301720", "4629287423061", "15802106905332", "53651151578187", "181257000301584" ]
[ "nonn", "easy" ]
10
0
3
[ "A027471", "A383136", "A383137", "A383138", "A383139" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-17T12:27:54
oeisdata/seq/A383/A383137.seq
e4a27d31640dfe420420ae01c0da9869
A383138
a(n) = Sum_{k=0..n} k^4 * 2^(n-k) * binomial(n,k).
[ "0", "1", "20", "189", "1320", "7785", "41148", "201285", "929232", "4100625", "17452260", "72098829", "290521080", "1146082041", "4439303820", "16923738645", "63619864992", "236206924065", "867305334708", "3152957079645", "11359168737480", "40589657212041", "143957705302620", "507079568653029" ]
[ "nonn", "easy" ]
10
0
3
[ "A027471", "A383136", "A383137", "A383138", "A383139" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-17T12:27:50
oeisdata/seq/A383/A383138.seq
65abcd2c22eacd593322db69c9525816
A383139
a(n) = Sum_{k=0..n} k^5 * 2^(n-k) * binomial(n,k).
[ "0", "1", "36", "447", "3768", "25725", "153468", "832923", "4213296", "20179449", "92510100", "409137399", "1755881064", "7345518453", "30059956332", "120676965075", "476358203232", "1852442299377", "7108046758404", "26948581794351", "101065091563800", "375297714478701", "1381124599327836", "5040775635099147" ]
[ "nonn", "easy" ]
8
0
3
[ "A027471", "A383136", "A383137", "A383138", "A383139" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-17T12:27:44
oeisdata/seq/A383/A383139.seq
3adc5207c3f0898d0429f0bab11df8f8
A383140
Triangle read by rows: the coefficients of polynomials (1/3^(m-n)) * Sum_{k=0..m} k^n * 2^(m-k) * binomial(m,k) in the variable m.
[ "1", "0", "1", "0", "2", "1", "0", "2", "6", "1", "0", "-6", "20", "12", "1", "0", "-30", "10", "80", "20", "1", "0", "42", "-320", "270", "220", "30", "1", "0", "882", "-1386", "-770", "1470", "490", "42", "1", "0", "954", "7308", "-15064", "2800", "5180", "952", "56", "1", "0", "-39870", "101826", "-39340", "-61992", "29820", "14364", "1680", "72", "1", "0", "-203958", "-40680", "841770", "-666820", "-86940", "139440", "34020", "2760", "90", "1" ]
[ "sign", "tabl" ]
36
0
5
[ "A000007", "A027471", "A129062", "A133494", "A179929", "A209849", "A212846", "A383136", "A383137", "A383138", "A383139", "A383140" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-18T08:44:25
oeisdata/seq/A383/A383140.seq
ba97be33e8c61ab725d44b77e3fd1631
A383141
Decimal expansion of the obliquity (in degrees) of a planet at which the annual instellations received by the poles and the equator are identical.
[ "5", "3", "8", "9", "6", "2", "3", "5", "8", "6", "2", "9", "5", "4", "2", "8", "7", "3", "1", "0", "1", "1", "2", "4", "6", "9", "2", "4", "2", "0", "8", "2", "1", "0", "8", "4", "5", "7", "9", "2", "0", "9", "5", "8", "3", "7", "4", "4", "7", "8", "6", "1", "1", "2", "2", "2", "7", "5", "5", "8", "9", "3", "4", "3", "6", "4", "9", "5", "4", "0", "1", "9", "1", "1", "0", "0", "1", "4", "7", "8", "7", "7", "7", "9", "8", "2", "6", "4", "7", "9", "8", "5", "9", "7", "7", "7", "5", "2", "5", "5", "7", "3", "4", "3", "5", "2", "7", "0", "1", "8", "5", "7", "4", "0", "5", "6", "5" ]
[ "nonn", "cons" ]
27
2
1
[ "A381254", "A383141" ]
null
Eliora Ben-Gurion, Apr 17 2025
2025-05-03T22:25:54
oeisdata/seq/A383/A383141.seq
4b6fab752e7efeb1040d1873d0549bd8
A383142
Smallest positive integer with shortest addition-subtraction chain of length n.
[ "1", "2", "3", "5", "7", "11", "19", "29", "53", "87", "151", "267", "461", "811", "1383", "2357", "4277", "7499", "14003", "25931", "44269", "87773", "152947", "271563" ]
[ "nonn", "hard", "more" ]
10
0
2
[ "A003064", "A128998", "A383001", "A383142", "A383143" ]
null
Jinyuan Wang, Apr 17 2025
2025-04-18T10:59:25
oeisdata/seq/A383/A383142.seq
03678383505ee891fec5dc1400426b4c
A383143
Number of positive integers with a shortest addition-subtraction chain of length n.
[ "1", "1", "2", "3", "5", "9", "16", "28", "49", "88", "156", "280", "499", "904", "1639", "2986", "5442", "9936", "18134" ]
[ "nonn", "hard", "more" ]
9
0
3
[ "A003065", "A128998", "A383002", "A383142", "A383143" ]
null
Jinyuan Wang, Apr 17 2025
2025-04-18T10:59:33
oeisdata/seq/A383/A383143.seq
b6d0f663cc4abfd99c5737e0576a7986
A383144
Number of abelian/medial racks of order n, up to isomorphism.
[ "1", "1", "2", "6", "18", "68", "329", "1965", "15455", "155902", "2064870", "35982366", "832699635", "25731050872" ]
[ "nonn", "hard", "more" ]
15
0
3
[ "A165200", "A176077", "A177886", "A178432", "A179010", "A181769", "A181770", "A181771", "A193024", "A196111", "A198147", "A225744", "A226172", "A226173", "A226174", "A226193", "A236146", "A242044", "A242275", "A243931", "A248908", "A254434", "A257351", "A383144", "A383145", "A383146", "A383829", "A383831" ]
null
Luc Ta, Apr 17 2025
2025-05-16T07:19:23
oeisdata/seq/A383/A383144.seq
597b9257226bd99dccb0222812c76d58
A383145
Number of GL-racks of order n, up to isomorphism.
[ "1", "1", "4", "13", "62", "308", "2132", "17268", "189373" ]
[ "hard", "more", "nonn" ]
12
0
3
[ "A165200", "A176077", "A177886", "A178432", "A179010", "A181769", "A181770", "A181771", "A193024", "A196111", "A198147", "A225744", "A226172", "A226173", "A226174", "A226193", "A236146", "A242044", "A242275", "A243931", "A248908", "A254434", "A257351", "A374939", "A374942", "A374943", "A374944", "A374945", "A374946", "A374947", "A383144", "A383145", "A383146" ]
null
Luc Ta, Apr 17 2025
2025-05-16T09:46:02
oeisdata/seq/A383/A383145.seq
ac1701b3588c85d6ecdf56abf4eb3350
A383146
Number of medial GL-racks of order n, up to isomorphism.
[ "1", "1", "4", "13", "61", "298", "2087", "16941", "187160" ]
[ "hard", "more", "nonn" ]
10
0
3
[ "A165200", "A176077", "A177886", "A178432", "A179010", "A181769", "A181770", "A181771", "A193024", "A196111", "A198147", "A225744", "A226172", "A226173", "A226174", "A226193", "A236146", "A242044", "A242275", "A243931", "A248908", "A254434", "A257351", "A374939", "A374942", "A374943", "A374944", "A374945", "A374946", "A374947", "A383144", "A383145", "A383146" ]
null
Luc Ta, Apr 17 2025
2025-05-16T09:45:32
oeisdata/seq/A383/A383146.seq
13c09f9132e7ad09d0ca5bf1065737a4
A383147
Sum of odd divisors m of n such that there is a divisor d of n with d < m < 2*d.
[ "0", "0", "0", "0", "0", "3", "0", "0", "0", "0", "0", "3", "0", "0", "5", "0", "0", "12", "0", "5", "0", "0", "0", "3", "0", "0", "0", "7", "0", "23", "0", "0", "0", "0", "7", "12", "0", "0", "0", "5", "0", "31", "0", "0", "29", "0", "0", "3", "0", "0", "0", "0", "0", "39", "0", "7", "0", "0", "0", "23", "0", "0", "9", "0", "0", "47", "0", "0", "0", "7", "0", "12", "0", "0", "30", "0", "11", "42", "0", "5", "0", "0", "0", "31", "0", "0", "0", "11", "0", "77", "13", "0", "0", "0", "0" ]
[ "nonn" ]
18
1
6
[ "A000593", "A237270", "A237271", "A237593", "A239657", "A379379", "A383147", "A383209" ]
null
Omar E. Pol, Apr 17 2025
2025-04-25T18:48:18
oeisdata/seq/A383/A383147.seq
1208bd32b0ad144409efb81cf80b8809
A383148
k-facile numbers: Numbers m such that the sum of the divisors of m is equal to 2*m+s where s is a product of distinct divisors of m.
[ "12", "18", "20", "24", "30", "40", "42", "54", "56", "60", "66", "78", "84", "88", "90", "102", "104", "114", "120", "132", "138", "140", "168", "174", "186", "196", "204", "222", "224", "234", "246", "252", "258", "264", "270", "280", "282", "308", "312", "318", "348", "354", "360", "364", "366", "368", "380", "402", "414", "420", "426", "438", "440", "456", "464", "468", "474", "476" ]
[ "nonn" ]
22
1
1
[ "A000203", "A000396", "A005101", "A181595", "A383148" ]
null
Joshua Zelinsky, Apr 17 2025
2025-04-24T18:27:20
oeisdata/seq/A383/A383148.seq
06b1efc486c3063db6d9d62100350ffe
A383149
Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) = (-1)^k * [m^k] (1/2^(m-n)) * Sum_{k=0..m} k^n * (-1)^m * 3^(m-k) * binomial(m,k).
[ "1", "0", "1", "0", "3", "1", "0", "12", "9", "1", "0", "66", "75", "18", "1", "0", "480", "690", "255", "30", "1", "0", "4368", "7290", "3555", "645", "45", "1", "0", "47712", "88536", "52290", "12705", "1365", "63", "1", "0", "608016", "1223628", "831684", "249585", "36120", "2562", "84", "1", "0", "8855040", "19019664", "14405580", "5073012", "915705", "87696", "4410", "108", "1" ]
[ "nonn", "tabl" ]
35
0
5
[ "A000007", "A001787", "A122704", "A123227", "A129062", "A178987", "A209849", "A383140", "A383149", "A383150", "A383151", "A383152", "A383155", "A383163", "A383164" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:44:21
oeisdata/seq/A383/A383149.seq
ed321630bfc9096af6944981d0279b39
A383150
a(n) = Sum_{k=0..n} k^3 * (-1)^k * 3^(n-k) * binomial(n,k).
[ "0", "-1", "2", "18", "64", "160", "288", "224", "-1024", "-6912", "-28160", "-95744", "-294912", "-851968", "-2351104", "-6266880", "-16252928", "-41222144", "-102629376", "-251527168", "-608174080", "-1453326336", "-3437232128", "-8055160832", "-18723373056", "-43201331200", "-99019128832", "-225586446336" ]
[ "sign", "easy" ]
18
0
3
[ "A001787", "A178987", "A383150", "A383151", "A383152", "A383155" ]
null
Seiichi Manyama, Apr 18 2025
2025-05-02T00:52:29
oeisdata/seq/A383/A383150.seq
228d658f64f20fd94d7f76362770b224
A383151
a(n) = Sum_{k=0..n} k^4 * (-1)^k * 3^(n-k) * binomial(n,k).
[ "0", "-1", "10", "36", "40", "-160", "-1152", "-4480", "-13568", "-34560", "-74240", "-123904", "-92160", "425984", "2867200", "11796480", "40763392", "128122880", "378667008", "1070858240", "2928148480", "7795113984", "20300431360", "51900317696", "130610626560", "324219699200", "795206483968", "1929715384320" ]
[ "sign", "easy" ]
18
0
3
[ "A001787", "A178987", "A383150", "A383151", "A383152", "A383155" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-23T16:21:30
oeisdata/seq/A383/A383151.seq
c3b13530c1908ae4f212e13baea86bbc
A383152
a(n) = Sum_{k=0..n} k^5 * (-1)^k * 3^(n-k) * binomial(n,k).
[ "0", "-1", "26", "18", "-272", "-1400", "-4032", "-7168", "-1024", "55296", "294400", "1086976", "3354624", "9132032", "22249472", "47923200", "85983232", "99155968", "-102629376", "-1237712896", "-5688524800", "-20775960576", "-67868033024", "-207022456832", "-602167836672", "-1690304512000", "-4613767954432" ]
[ "sign", "easy" ]
28
0
3
[ "A001787", "A178987", "A383150", "A383151", "A383152", "A383155" ]
null
Seiichi Manyama, Apr 18 2025
2025-05-01T23:52:37
oeisdata/seq/A383/A383152.seq
5f9c3aa56d4117555897edc0ff6846a7
A383153
Square array read by antidiagonals: A(m,n) is the number of 2m-by-2n fers-wazir tours.
[ "2", "1", "1", "1", "2", "1", "1", "4", "4", "1", "1", "9", "22", "9", "1", "1", "23", "124", "124", "23", "1", "1", "62", "818", "1620", "818", "62", "1", "1", "170", "6004", "25111", "25111", "6004", "170", "1", "1", "469", "46488", "455219", "882130", "455219", "46488", "469", "1", "1", "1297", "367880", "9103712", "36979379", "36979379", "9103712", "367880", "1297", "1" ]
[ "nonn", "tabl" ]
58
1
1
[ "A339190", "A383153", "A383154" ]
null
Don Knuth, Apr 18 2025
2025-04-25T14:31:07
oeisdata/seq/A383/A383153.seq
de8d6d65709a52e09b111e0e01dd7739
A383154
The number of 2n-by-2n fers-wazir tours.
[ "2", "2", "22", "1620", "882130", "3465050546" ]
[ "nonn", "more" ]
13
1
1
[ "A140519", "A383153", "A383154" ]
null
Don Knuth, Apr 18 2025
2025-04-18T13:57:51
oeisdata/seq/A383/A383154.seq
7a5229ee02d5cc0f9c69e98b1e430499
A383155
a(n) = Sum_{k=0..n} k^6 * (-1)^k * 3^(n-k) * binomial(n,k).
[ "0", "-1", "58", "-180", "-1304", "-2920", "1008", "34496", "163840", "525312", "1285120", "2241536", "1124352", "-12113920", "-72052736", "-282378240", "-924581888", "-2699493376", "-7201751040", "-17666670592", "-39507722240", "-77918109696", "-121883328512", "-78622228480", "453588811776", "2904974950400", "11885785120768" ]
[ "sign", "easy" ]
15
0
3
[ "A001787", "A178987", "A383150", "A383151", "A383152", "A383155" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-23T13:24:30
oeisdata/seq/A383/A383155.seq
9781197c82dcb22970e5f3cf2cae31df
A383156
The sum of the maximum exponents in the prime factorizations of the divisors of n.
[ "0", "1", "1", "3", "1", "3", "1", "6", "3", "3", "1", "7", "1", "3", "3", "10", "1", "7", "1", "7", "3", "3", "1", "13", "3", "3", "6", "7", "1", "7", "1", "15", "3", "3", "3", "13", "1", "3", "3", "13", "1", "7", "1", "7", "7", "3", "1", "21", "3", "7", "3", "7", "1", "13", "3", "13", "3", "3", "1", "15", "1", "3", "7", "21", "3", "7", "1", "7", "3", "7", "1", "22", "1", "3", "7", "7", "3", "7", "1", "21", "10", "3", "1" ]
[ "nonn", "easy" ]
10
1
4
[ "A000005", "A001221", "A001620", "A005117", "A013661", "A033150", "A034444", "A051903", "A073184", "A118914", "A252505", "A306016", "A309307", "A383156", "A383157", "A383158", "A383159" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:39:02
oeisdata/seq/A383/A383156.seq
3f8b107cbe0c54bb268e111409081ae0
A383157
a(n) is the numerator of the mean of the maximum exponents in the prime factorizations of the divisors of n.
[ "0", "1", "1", "1", "1", "3", "1", "3", "1", "3", "1", "7", "1", "3", "3", "2", "1", "7", "1", "7", "3", "3", "1", "13", "1", "3", "3", "7", "1", "7", "1", "5", "3", "3", "3", "13", "1", "3", "3", "13", "1", "7", "1", "7", "7", "3", "1", "21", "1", "7", "3", "7", "1", "13", "3", "13", "3", "3", "1", "5", "1", "3", "7", "3", "3", "7", "1", "7", "3", "7", "1", "11", "1", "3", "7", "7", "3", "7", "1", "21", "2", "3", "1", "5", "3" ]
[ "nonn", "easy", "frac" ]
10
1
6
[ "A000005", "A001248", "A051903", "A118914", "A308043", "A345231", "A361062", "A383156", "A383157", "A383158" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:39:14
oeisdata/seq/A383/A383157.seq
c7adfecc18a75672f1ca34429119b78e
A383158
a(n) is the denominator of the mean of the maximum exponents in the prime factorizations of the divisors of n.
[ "1", "2", "2", "1", "2", "4", "2", "2", "1", "4", "2", "6", "2", "4", "4", "1", "2", "6", "2", "6", "4", "4", "2", "8", "1", "4", "2", "6", "2", "8", "2", "2", "4", "4", "4", "9", "2", "4", "4", "8", "2", "8", "2", "6", "6", "4", "2", "10", "1", "6", "4", "6", "2", "8", "4", "8", "4", "4", "2", "4", "2", "4", "6", "1", "4", "8", "2", "6", "4", "8", "2", "6", "2", "4", "6", "6", "4", "8", "2", "10", "1", "4", "2", "4", "4", "4", "4" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A000005", "A051903", "A056798", "A118914", "A383156", "A383157", "A383158" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:39:40
oeisdata/seq/A383/A383158.seq
0a25497b97de8e8b99c71f164aff6091
A383159
The sum of the maximum exponents in the prime factorizations of the unitary divisors of n.
[ "0", "1", "1", "2", "1", "3", "1", "3", "2", "3", "1", "5", "1", "3", "3", "4", "1", "5", "1", "5", "3", "3", "1", "7", "2", "3", "3", "5", "1", "7", "1", "5", "3", "3", "3", "6", "1", "3", "3", "7", "1", "7", "1", "5", "5", "3", "1", "9", "2", "5", "3", "5", "1", "7", "3", "7", "3", "3", "1", "11", "1", "3", "5", "6", "3", "7", "1", "5", "3", "7", "1", "8", "1", "3", "5", "5", "3", "7", "1", "9", "4", "3", "1", "11", "3", "3", "3" ]
[ "nonn", "easy" ]
11
1
4
[ "A005117", "A032741", "A034444", "A051903", "A056671", "A077610", "A305611", "A325770", "A365498", "A365499", "A383156", "A383159", "A383160", "A383161" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:40:04
oeisdata/seq/A383/A383159.seq
ac7ec3ae5f50581a8b089881e0a32f0e
A383160
a(n) is the numerator of the mean of the maximum exponents in the prime factorizations of the unitary divisors of n.
[ "0", "1", "1", "1", "1", "3", "1", "3", "1", "3", "1", "5", "1", "3", "3", "2", "1", "5", "1", "5", "3", "3", "1", "7", "1", "3", "3", "5", "1", "7", "1", "5", "3", "3", "3", "3", "1", "3", "3", "7", "1", "7", "1", "5", "5", "3", "1", "9", "1", "5", "3", "5", "1", "7", "3", "7", "3", "3", "1", "11", "1", "3", "5", "3", "3", "7", "1", "5", "3", "7", "1", "2", "1", "3", "5", "5", "3", "7", "1", "9", "2", "3", "1", "11", "3", "3", "3" ]
[ "nonn", "easy", "frac" ]
9
1
6
[ "A000961", "A001248", "A005117", "A034444", "A051903", "A077610", "A118914", "A126706", "A296082", "A345288", "A383057", "A383058", "A383157", "A383158", "A383159", "A383160", "A383161" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:40:20
oeisdata/seq/A383/A383160.seq
bbf4f693d0197047b3851b39ad2ad46b
A383161
a(n) is the denominator of the mean of the maximum exponents in the prime factorizations of the unitary divisors of n.
[ "1", "2", "2", "1", "2", "4", "2", "2", "1", "4", "2", "4", "2", "4", "4", "1", "2", "4", "2", "4", "4", "4", "2", "4", "1", "4", "2", "4", "2", "8", "2", "2", "4", "4", "4", "2", "2", "4", "4", "4", "2", "8", "2", "4", "4", "4", "2", "4", "1", "4", "4", "4", "2", "4", "4", "4", "4", "4", "2", "8", "2", "4", "4", "1", "4", "8", "2", "4", "4", "8", "2", "1", "2", "4", "4", "4", "4", "8", "2", "4", "1", "4", "2", "8", "4", "4", "4", "4" ]
[ "nonn", "easy", "frac" ]
8
1
2
[ "A034444", "A051903", "A056798", "A077610", "A118914", "A383158", "A383159", "A383160", "A383161" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:38:27
oeisdata/seq/A383/A383161.seq
dbbcda0ce2a2263334c983954714edfc
A383162
Consecutive states of the linear congruential pseudo-random number generator (7200*s + 1) mod 23^4 when started at s=1.
[ "1", "7201", "76616", "68590", "208477", "247118", "20523", "9553", "220556", "185367", "80672", "168326", "235671", "155218", "164488", "26489", "149080", "185766", "155062", "160652", "111548", "1931", "190992", "3727", "249506", "143822", "106701", "83656", "105369", "7850", "271960", "64524", "36741", "85456", "192683" ]
[ "nonn", "easy" ]
18
1
2
[ "A383129", "A383162", "A384081" ]
null
Sean A. Irvine, Jun 13 2025
2025-06-18T12:20:36
oeisdata/seq/A383/A383162.seq
2bac7e4d08a49a2002abf6afb3d90fa9
A383163
Expansion of e.g.f. log(1 - (exp(2*x) - 1)/2)^2 / 2.
[ "0", "0", "1", "9", "75", "690", "7290", "88536", "1223628", "19019664", "328908720", "6268688448", "130615236576", "2954657491968", "72128519473920", "1890266313945600", "52937770062975744", "1577901064699594752", "49877742373556336640", "1666688195869095124992", "58704547943954039672832" ]
[ "nonn" ]
12
0
4
[ "A000254", "A383149", "A383163" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T10:05:53
oeisdata/seq/A383/A383163.seq
24612671d2a1c2ae01c2cc4957a38ddc
A383164
Expansion of e.g.f. -log(1 - (exp(2*x) - 1)/2)^3 / 6.
[ "0", "0", "0", "1", "18", "255", "3555", "52290", "831684", "14405580", "271688580", "5562400800", "123123764808", "2933953637472", "74953425290016", "2044855241694720", "59361121229581440", "1827578437315965696", "59494057195888597248", "2042194772007257103360", "73731225467600254686720" ]
[ "nonn" ]
11
0
5
[ "A000399", "A383149", "A383164", "A383166" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T10:10:32
oeisdata/seq/A383/A383164.seq
5035ec32f97c0034cca4beee6aa76531
A383165
Expansion of e.g.f. log(1 + (exp(2*x) - 1)/2)^2 / 2.
[ "0", "0", "1", "3", "3", "-10", "-30", "112", "588", "-2448", "-18960", "87296", "911328", "-4599296", "-61152000", "335523840", "5464904448", "-32363874304", "-627708979200", "3987441516544", "90133968949248", "-610866587369472", "-15823700431503360", "113884455221854208", "3334995367266582528", "-25385597162671308800" ]
[ "sign" ]
10
0
4
[ "A009392", "A209849", "A383163", "A383165" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:44:46
oeisdata/seq/A383/A383165.seq
852d41a7f2d7adf609094eb5fcb09dc0
A383166
Expansion of e.g.f. log(1 + (exp(2*x) - 1)/2)^3 / 6.
[ "0", "0", "0", "1", "6", "15", "-15", "-210", "28", "5292", "4140", "-208560", "-369864", "11847264", "33630688", "-917280000", "-3642944640", "92903375616", "479824306944", "-11926470604800", "-76477342307840", "1892813347934208", "14591875555074048", "-363945109924577280", "-3293838565260693504", "83374884181664563200" ]
[ "sign" ]
9
0
5
[ "A209849", "A383164", "A383166" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:44:42
oeisdata/seq/A383/A383166.seq
8aba7255127be54b52300af7f5c7656e
A383167
Primes p such that p + 4, p + 10, p + 12, p + 18 and p + 22 are also primes.
[ "19", "1279", "5839", "32359", "75979", "88789", "113149", "138559", "229759", "246919", "357649", "433249", "460969", "590119", "595939", "839599", "855709", "1257229", "1266259", "1287739", "1652869", "1749259", "1880929", "2428879", "2580649", "2882479", "3245569", "3300949", "3753349", "3809149", "3939769" ]
[ "nonn" ]
51
1
1
[ "A000040", "A001223", "A022008", "A140565", "A383167" ]
null
Alexander Yutkin, Apr 25 2025
2025-05-02T22:36:46
oeisdata/seq/A383/A383167.seq
afcd34dc587fe7dfec1efeeda53d079b
A383168
Triangle T(n,k) read by rows: For closed chains of identical regular m-gons with connecting inner vertices lying n vertices apart, the n-th row lists the possible m in ascending order; n>=0, 1<=k<=d(8+4n).
[ "5", "6", "8", "12", "7", "8", "9", "10", "12", "18", "9", "10", "12", "16", "24", "11", "12", "14", "15", "20", "30", "13", "14", "15", "16", "18", "20", "24", "36", "15", "16", "18", "21", "28", "42", "17", "18", "20", "24", "32", "48", "19", "20", "21", "22", "24", "27", "30", "36", "54", "21", "22", "24", "25", "28", "30", "40", "60", "23", "24", "26", "33", "44", "66" ]
[ "nonn", "tabf" ]
13
1
1
[ "A047244", "A366872", "A383168", "A383169" ]
null
Manfred Boergens, Apr 18 2025
2025-05-09T01:31:31
oeisdata/seq/A383/A383168.seq
4555b78cff7f8fe19042d41859e58fef
A383169
Triangle T(n,k) read by rows: For closed chains of j identical regular polygons with connecting inner vertices lying n vertices apart, the n-th row lists the possible j in descending order; n>=0, 1<=k<=d(8+4n).
[ "10", "6", "4", "3", "14", "8", "6", "5", "4", "3", "18", "10", "6", "4", "3", "22", "12", "7", "6", "4", "3", "26", "14", "10", "8", "6", "5", "4", "3", "30", "16", "9", "6", "4", "3", "34", "18", "10", "6", "4", "3", "38", "20", "14", "11", "8", "6", "5", "4", "3", "42", "22", "12", "10", "7", "6", "4", "3", "46", "24", "13", "6", "4", "3", "50", "26", "18", "14", "10", "8", "6", "5", "4", "3" ]
[ "nonn", "tabf" ]
10
1
1
[ "A366872", "A383168", "A383169" ]
null
Manfred Boergens, Apr 18 2025
2025-05-01T19:59:08
oeisdata/seq/A383/A383169.seq
f28d9780c286ed8abd26003b2937f610
A383170
Expansion of e.g.f. -log(1 + log(1 - 2*x)/2).
[ "0", "1", "3", "16", "122", "1208", "14704", "212336", "3547984", "67337728", "1430990976", "33664165632", "868592478720", "24390846882816", "740570519159808", "24177326011834368", "844599686386919424", "31438092340685144064", "1242230898248798896128", "51933512200489564962816", "2290351520336982559358976" ]
[ "nonn" ]
11
0
3
[ "A003713", "A227917", "A383170", "A383171", "A383172" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T10:16:21
oeisdata/seq/A383/A383170.seq
f051fe91d8989b4297145265a0e6bfcb
A383171
Expansion of e.g.f. log(1 + log(1 - 2*x)/2)^2 / 2.
[ "0", "0", "1", "9", "91", "1090", "15298", "247352", "4537132", "93195696", "2120623984", "52973194560", "1441635171040", "42464913775232", "1346297567292416", "45715740985471744", "1655552663185480448", "63698261991541393408", "2595107348458704209920", "111613055867327344582656" ]
[ "nonn" ]
11
0
4
[ "A341587", "A383163", "A383170", "A383171", "A383172" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T10:22:17
oeisdata/seq/A383/A383171.seq
99dce5dce06d3949a1d359ceccef6e87
A383172
Expansion of e.g.f. -log(1 + log(1 - 2*x)/2)^3 / 6.
[ "0", "0", "0", "1", "18", "295", "5115", "96838", "2012724", "45825148", "1137703140", "30643915984", "891001127016", "27835772321344", "930387252759328", "33141746095999552", "1253756533365348992", "50210676392866266880", "2122613151692627299584", "94470824166941637093376" ]
[ "nonn" ]
10
0
5
[ "A341588", "A383164", "A383170", "A383171", "A383172" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:44:28
oeisdata/seq/A383/A383172.seq
ac9680a5c7d0399394d45a6625d48d8a
A383173
Decimal expansion of the area of the biggest little decagon.
[ "7", "4", "9", "1", "3", "7", "3", "4", "5", "8", "7", "7", "8", "3", "0", "2", "7", "0", "6", "2", "2", "7", "1", "9", "8", "2", "7", "8", "8", "2", "7", "0", "1", "4", "5", "1", "9", "4", "9", "1", "5", "2", "5", "8", "0", "8", "1", "5", "0", "2", "5", "4", "5", "7", "7", "2", "1", "0", "5", "5", "3", "8", "2", "3", "2", "4", "2", "9", "2", "7", "8", "5", "6", "1", "1", "1", "9", "0", "0", "7", "7", "5", "1", "9", "8", "6", "0", "3", "7", "2", "5", "7", "6", "8", "5", "8", "6", "8", "5", "8", "7", "7", "2", "7", "5", "6", "7", "7", "8", "9", "3", "0", "8", "6", "7", "7", "6", "2", "3" ]
[ "nonn", "cons" ]
12
0
1
[ "A111969", "A381252", "A383173" ]
null
Eric W. Weisstein, Apr 18 2025
2025-06-14T21:42:21
oeisdata/seq/A383/A383173.seq
383b7772c9cf00e8d1c832ddfd4b417b
A383174
Permutation of the natural numbers formed by ordering by max(gpfi,bigomega), then bigomega, then numerically, where gpfi(k) = A061395(k) and bigomega(k) = A001222(k).
[ "1", "2", "3", "4", "6", "9", "5", "10", "15", "25", "8", "12", "18", "20", "27", "30", "45", "50", "75", "125", "7", "14", "21", "35", "49", "28", "42", "63", "70", "98", "105", "147", "175", "245", "343", "16", "24", "36", "40", "54", "56", "60", "81", "84", "90", "100", "126", "135", "140", "150", "189", "196", "210", "225", "250", "294", "315", "350", "375", "441", "490", "525" ]
[ "nonn" ]
55
1
2
[ "A001222", "A061395", "A263297", "A344844", "A383174" ]
null
Bassam Abdul-Baki, Apr 18 2025
2025-05-02T22:28:45
oeisdata/seq/A383/A383174.seq
4f70a12047dd24bb77641860cd6b5b66
A383175
Number of compositions of n such that any fixed point k can be k different colors.
[ "1", "1", "2", "5", "10", "22", "48", "101", "213", "450", "945", "1961", "4064", "8385", "17242", "35332", "72141", "146924", "298552", "605377", "1225277", "2475912", "4995754", "10067848", "20267680", "40762951", "81916919", "164504411", "330155437", "662265817", "1327860471", "2661376529", "5332341881", "10680912173" ]
[ "nonn", "easy" ]
13
0
3
[ "A011782", "A088305", "A238349", "A238350", "A238351", "A335713", "A352512", "A383175" ]
null
John Tyler Rascoe, Apr 18 2025
2025-04-21T16:27:11
oeisdata/seq/A383/A383175.seq
5cf26780acadfe5288a0acfd63b49630
A383176
If p = A002313(n) is a prime such that p = x^2 + y^2, then a(n) is the largest integer k that satisfies x^2 + y^2 - k*x*y > 0.
[ "1", "2", "2", "4", "2", "6", "2", "3", "2", "3", "2", "2", "10", "3", "2", "3", "2", "2", "6", "2", "2", "14", "7", "2", "4", "16", "2", "2", "3", "8", "2", "2", "2", "3", "2", "2", "2", "3", "20", "6", "2", "2", "3", "5", "2", "4", "2", "2", "2", "2", "24", "3", "5", "2", "2", "6", "2", "4", "2", "26", "5", "2", "13", "3", "2", "2", "2", "2", "5", "2", "3", "2", "7", "5", "2", "2", "2", "3", "2", "7", "5", "2", "2", "3" ]
[ "nonn" ]
19
1
2
[ "A002313", "A002330", "A002331", "A383176" ]
null
Gonzalo Martínez, Apr 18 2025
2025-04-27T01:12:35
oeisdata/seq/A383/A383176.seq
0678bb1895d5d33d7f6270bb1b07e3c7
A383177
Sphenic numbers k such that floor(log(k)/log(lpf(k))) = 1+floor(log(k)/log(p)) for all primes p | k such that p > lpf(k), where lpf = A020639(k).
[ "1001", "1309", "1547", "1729", "2093", "2261", "3553", "4199", "4301", "4807", "5681", "6061", "6479", "7337", "7843", "8671", "9269", "9361", "9889", "10373", "10879", "11063", "11339", "11687", "11803", "11891", "12121", "12617", "13079", "13717", "13949", "13981", "14911", "15283", "15457", "16211", "16523", "17081", "17329", "17719" ]
[ "nonn" ]
16
1
1
[ "A005117", "A007304", "A010846", "A162306", "A380995", "A381250", "A382022", "A383177" ]
null
Michael De Vlieger, Apr 21 2025
2025-06-07T11:58:51
oeisdata/seq/A383/A383177.seq
09ede25eda6a1fe30e80225be27ce9d3
A383178
Numbers k such that omega(k) = 4 and p^omega(k) < k^(1/4) < lpf(k)^(omega(k)+1) for all primes p | k such that p > lpf(k), where lpf = A020639(k).
[ "81719", "268801", "565471", "626603", "631997", "657169", "700321", "799459", "838457", "893513", "916453", "1108927", "1212083", "1239389", "1271209", "1354681", "1366817", "1408637", "1420763", "1500313", "1527619", "1574359", "1602137", "1639877", "1700557", "1719871", "1751173", "1758203", "1775341", "1783511", "1843969" ]
[ "nonn" ]
7
1
1
[ "A010846", "A020639", "A162306", "A383177", "A383178" ]
null
Michael De Vlieger, May 09 2025
2025-05-16T00:55:54
oeisdata/seq/A383/A383178.seq
bb93f5ed0035d2fd618ef6ac06b79796
A383179
Numbers k such that omega(k) = 5 and p^omega(k) < k^(1/5) < lpf(k)^(omega(k)+1) for all primes p | k such that p > lpf(k), where lpf = A020639(k).
[ "101007559", "112442377", "145352341", "370621421", "392748073", "396181519", "403811399", "496492847", "510478561", "530733733", "540954893", "545683979", "552435703", "578262127", "580407131", "585416939", "590534717", "594163571", "620435209", "625790521", "633456391", "635140369", "643418423", "651300233" ]
[ "nonn" ]
7
1
1
[ "A010846", "A020639", "A162306", "A383177", "A383178", "A383179" ]
null
Michael De Vlieger, May 09 2025
2025-05-16T00:55:47
oeisdata/seq/A383/A383179.seq
1debc115b845f3eb66be8974645d0afb
A383180
Irregular table T(n,k) = A010846(A019565(2^n + k)).
[ "1", "2", "2", "5", "2", "6", "5", "18", "2", "6", "5", "19", "5", "20", "16", "68", "2", "7", "6", "22", "5", "21", "18", "77", "5", "22", "17", "79", "16", "74", "60", "283", "2", "7", "6", "23", "5", "23", "18", "80", "5", "22", "18", "82", "16", "78", "62", "295", "5", "24", "19", "87", "16", "82", "64", "315", "15", "80", "62", "316", "55", "290", "226", "1161" ]
[ "nonn", "tabf" ]
8
0
2
[ "A005117", "A010846", "A019565", "A363061", "A383180" ]
null
Michael De Vlieger, May 09 2025
2025-05-14T01:24:17
oeisdata/seq/A383/A383180.seq
523d54c2e7136e51fefe54cdf5fadede
A383181
Family of 2-colorings of {1..7824} with no monochromatic Pythagorean triples.
[ "0", "0", "2", "0", "1", "0", "1", "2", "0", "1", "0", "2", "2", "0", "1", "1", "0", "1", "0", "2", "2", "0", "0", "2", "2", "0", "1", "1", "1", "2", "0", "1", "0", "1", "1", "0", "0", "0", "2", "2", "1", "1", "2", "2", "2", "0", "0", "2", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "0", "1", "2", "2", "2", "1", "1", "1", "0", "2", "2", "1", "0", "1", "0", "1", "1", "1", "2", "2", "0", "2", "1", "2", "0", "1", "1", "1", "1", "1", "1", "1", "2", "0", "1", "0", "2", "2", "2", "2", "1", "2" ]
[ "nonn", "fini", "full" ]
31
1
3
[ "A009003", "A156685", "A224921", "A272709", "A383181" ]
null
David Dewan, Apr 18 2025
2025-05-19T00:07:14
oeisdata/seq/A383/A383181.seq
395163ce0d67778072727178e165fe77
A383182
a(n) = 2^n - A129629(n+1).
[ "0", "1", "1", "1", "2", "1", "1", "5", "1", "1", "9", "1", "4", "16", "1", "1", "33", "11", "1", "65", "1", "1", "142", "1", "8", "257", "1", "35", "513", "1", "1", "1038", "67", "1", "2049", "1", "1", "4220", "39", "1", "8192", "1", "259", "16385", "1", "71", "32769", "515", "1", "65550", "1", "1", "132211", "1", "1", "262145", "1", "2051", "524302", "263", "32", "1048577", "4096", "1", "2097153", "1", "519", "4202480", "1", "1" ]
[ "nonn" ]
9
0
5
[ "A129629", "A383182" ]
null
M. F. Hasler, May 27 2025
2025-06-01T18:52:05
oeisdata/seq/A383/A383182.seq
e515251b6cd67393b4a02685b4108eba
A383183
Square spiral numbers of the n-th grid point visited by a king always moving to the unvisited point labeled with the smallest possible prime or else composite number.
[ "0", "2", "3", "5", "7", "23", "47", "79", "48", "24", "8", "1", "11", "13", "31", "29", "53", "27", "9", "10", "26", "25", "49", "83", "50", "51", "52", "28", "12", "30", "54", "55", "89", "131", "179", "129", "87", "127", "85", "84", "124", "173", "229", "293", "227", "169", "223", "167", "119", "80", "81", "82", "122", "120", "121", "168", "170", "171", "123", "172", "228", "292", "226", "224", "225", "287", "359", "439" ]
[ "nonn", "walk", "fini", "full" ]
15
0
2
[ "A316328", "A335856", "A383183", "A383184", "A383185" ]
null
M. F. Hasler, May 13 2025
2025-05-20T15:33:00
oeisdata/seq/A383/A383183.seq
23bf754dee93f8e5eadb06e458a56639
A383184
Diamond spiral numbers of the grid points visited by a king always moving to the unvisited point labeled with the smallest possible prime or else composite number.
[ "0", "2", "3", "11", "23", "4", "5", "13", "12", "24", "41", "61", "40", "59", "83", "60", "84", "113", "85", "86", "62", "25", "26", "43", "14", "1", "7", "17", "31", "8", "19", "9", "10", "37", "21", "20", "53", "34", "33", "18", "32", "71", "97", "127", "72", "73", "50", "49", "48", "47", "29", "6", "15", "16", "30", "69", "68", "67", "28", "27", "44", "89", "64", "63", "42", "87", "88", "149", "116", "115", "114", "146", "223", "182", "181", "144", "179", "112", "111", "110", "109", "58", "38", "22", "57", "56", "79", "107", "139", "80", "81", "82", "39" ]
[ "nonn", "walk", "fini", "full" ]
8
0
2
[ "A305258", "A383183", "A383184" ]
null
M. F. Hasler, May 13 2025
2025-05-24T17:53:58
oeisdata/seq/A383/A383184.seq
fb862f6f96d0c31b03c9686988d3ab3e
A383185
Number of the square visited by a king moving on a spirally numbered board always to the lowest available unvisited square, when a wall delimiting the spiral must be crossed on each move.
[ "0", "3", "13", "2", "10", "1", "7", "21", "6", "18", "4", "14", "32", "12", "28", "11", "27", "9", "23", "8", "22", "44", "20", "40", "19", "5", "17", "37", "16", "34", "15", "33", "59", "31", "57", "30", "54", "29", "53", "85", "51", "25", "47", "24", "46", "76", "45", "75", "43", "73", "42", "70", "41", "69", "39", "67", "38", "66", "36", "62", "35", "61", "95", "60", "94", "58", "92", "56", "88", "55", "87", "127", "86", "52", "26" ]
[ "nonn", "walk" ]
38
0
2
[ "A033638", "A316328", "A316667", "A335856", "A336038", "A375925", "A383185", "A383186" ]
null
M. F. Hasler, May 12 2025
2025-05-21T11:21:21
oeisdata/seq/A383/A383185.seq
e038c1b49572b4d7891c3de821096dce
A383186
Inverse permutation to A383185 (square spiral numbers of king filling the two-dimensional grid always crossing the spiral's wall).
[ "0", "5", "3", "1", "10", "25", "8", "6", "19", "17", "4", "15", "13", "2", "11", "30", "28", "26", "9", "24", "22", "7", "20", "18", "43", "41", "74", "16", "14", "37", "35", "33", "12", "31", "29", "60", "58", "27", "56", "54", "23", "52", "50", "48", "21", "46", "44", "42", "79", "77", "75", "40", "73", "38", "36", "69", "67", "34", "65", "32", "63", "61", "59", "100", "98", "147", "57", "55", "94", "53", "51", "90", "88", "49", "86" ]
[ "nonn" ]
11
0
2
[ "A383185", "A383186" ]
null
M. F. Hasler, May 12 2025
2025-05-21T23:24:00
oeisdata/seq/A383/A383186.seq
b753a544f66894ff177a35306bf2ec8b
A383187
Diamond spiral number of the n-th point visited by the king moving on the two-dimensional grid always to the earliest unvisited point on the spiral, not immediately preceding or following on the spiral.
[ "0", "2", "7", "1", "4", "11", "3", "9", "19", "8", "17", "30", "16", "6", "14", "5", "12", "23", "38", "22", "10", "20", "34", "52", "33", "18", "31", "48", "69", "47", "29", "15", "27", "43", "26", "13", "24", "39", "58", "81", "57", "37", "21", "35", "53", "75", "101", "74", "51", "32", "49", "70", "95", "124", "94", "68", "46", "28", "44", "64", "88", "63", "42", "25", "40", "59", "82", "109", "140", "108", "80", "56", "36", "54", "76" ]
[ "nonn", "walk" ]
13
0
2
[ "A305258", "A383185", "A383187", "A383189" ]
null
M. F. Hasler, May 12 2025
2025-05-20T15:32:20
oeisdata/seq/A383/A383187.seq
ca22aa1eb60f1608b3242a2104106348
A383188
Irregular table, read by rows, where row z = 2, 3, 4, ... lists pairs (y, x) such that x + y/z = concat(y, x)/z with 0 < y < z, gcd(y, z) = 1, and primitive x, cf. comments.
[ "1", "9", "2", "9", "1", "3", "3", "9", "4", "9", "5", "9", "2", "3", "4", "6", "6", "9", "1", "142857", "3", "428571", "5", "714285", "7", "9", "8", "9", "3", "3", "7", "7", "9", "9", "10", "9", "5", "45", "7", "63", "11", "9", "4", "3", "8", "6", "12", "9", "3", "230769", "5", "384615", "7", "538461", "11", "846153", "13", "9", "2", "142857", "4", "285714", "8", "571428", "14", "9", "5", "3", "15", "9", "16", "9", "5", "2941176470588235", "7", "4117647058823529", "11", "6470588235294117", "13", "7647058823529411", "17", "9", "2", "1", "4", "2", "6", "3", "8", "4", "10", "5", "12", "6", "14", "7", "16", "8", "18", "9" ]
[ "nonn" ]
14
2
2
[ "A036275", "A060284", "A383188" ]
null
M. F. Hasler, May 03 2025
2025-05-16T18:11:43
oeisdata/seq/A383/A383188.seq
2d48291efb728b41451223ace618cdc8
A383189
Inverse permutation to A383187 (diamond spiral numbers of a king moving on the infinite two-dimensional grid, not to the point numbered a(n)+-1).
[ "0", "3", "1", "6", "4", "15", "13", "2", "9", "7", "20", "5", "16", "35", "14", "31", "12", "10", "25", "8", "21", "42", "19", "17", "36", "63", "34", "32", "57", "30", "11", "26", "49", "24", "22", "43", "72", "41", "18", "37", "64", "99", "62", "33", "58", "91", "56", "29", "27", "50", "81", "48", "23", "44", "73", "110", "71", "40", "38", "65", "100", "143", "98", "61", "59", "92", "133", "90", "55", "28", "51", "82", "121", "80" ]
[ "nonn" ]
13
0
2
[ "A383187", "A383189" ]
null
M. F. Hasler, May 12 2025
2025-05-23T01:08:04
oeisdata/seq/A383/A383189.seq
9e04f89e8ea407aeaec21936477df715
A383190
a(2n) and a(2n+1) are the square spiral numbers of the position on which the (n+1)th domino is placed, when tiling the plane by placing the dominos always as near as possible to the origin and so that no two dominos share a long side. Inverse permutation of A383191.
[ "0", "1", "3", "4", "5", "6", "7", "22", "2", "11", "8", "9", "10", "27", "14", "13", "18", "17", "15", "16", "19", "20", "21", "44", "23", "46", "12", "29", "24", "25", "33", "34", "39", "40", "45", "76", "28", "53", "32", "31", "38", "37", "26", "51", "35", "36", "41", "42", "43", "74", "47", "78", "52", "85", "60", "59", "68", "67", "61", "62", "69", "70", "75", "114", "77", "116", "30", "55", "48", "49", "54", "87", "58", "57", "66", "65" ]
[ "nonn" ]
20
0
3
[ "A174344", "A316328", "A383190", "A383191" ]
null
M. F. Hasler, Apr 18 2025
2025-04-23T10:35:15
oeisdata/seq/A383/A383190.seq
5b41df890d7a8215b499c1b4a8ae56ff
A383191
a(n) is the number on the n-th position on the square spiral on the plane tiled with dominoes always placed nearest to the origin and so that no two dominos share a long side. Inverse permutation of A383190.
[ "0", "1", "8", "2", "3", "4", "5", "6", "10", "11", "12", "9", "26", "15", "14", "18", "19", "17", "16", "20", "21", "22", "7", "24", "28", "29", "42", "13", "36", "27", "66", "39", "38", "30", "31", "44", "45", "41", "40", "32", "33", "46", "47", "48", "23", "34", "25", "50", "68", "69", "76", "43", "52", "37", "70", "67", "108", "73", "72", "55", "54", "58", "59", "80", "81", "75", "74", "57", "56", "60", "61", "84", "85", "86", "49", "62" ]
[ "nonn" ]
13
0
3
[ "A174344", "A316328", "A316667", "A383190", "A383191" ]
null
M. F. Hasler, Apr 18 2025
2025-04-23T10:35:36
oeisdata/seq/A383/A383191.seq
faeb054b1648fcfa1623f5419e9856aa
A383192
a(n) is the number of possible choices for the first n terms of a "mean-central" sequence, where a monotonically increasing sequence of positive integers {b(n)} is called "mean-central" if for each positive integer k, the arithmetic mean of the first b(k) terms is exactly b(k).
[ "1", "2", "2", "3", "3", "4", "8", "16", "20", "25", "27", "48", "72", "107", "149", "260", "372", "511", "653", "1032", "1192", "1713", "2218", "3992", "5504", "7729", "10452", "16397", "21700", "32292", "43742", "72859", "98926", "143759", "187703", "284689", "368374", "526256", "729299", "1315303" ]
[ "nonn", "more" ]
27
1
2
[ "A383192", "A383193", "A383194" ]
null
Yifan Xie, Apr 19 2025
2025-04-29T13:16:59
oeisdata/seq/A383/A383192.seq
a07e3f698a2b2be383b36e6f2bb4ddc0
A383193
The lexicographically earliest "mean-central" sequence, as is defined in A383192.
[ "1", "3", "5", "6", "10", "11", "12", "13", "19", "20", "21", "23", "25", "26", "27", "28", "36", "37", "38", "39", "41", "42", "46", "47", "49", "51", "53", "55", "56", "57", "58", "59", "69", "70", "71", "72", "73", "75", "77", "78", "82", "83", "84", "85", "91", "92", "93", "94", "98", "99", "101", "102", "106", "107", "109", "111", "113", "115", "117", "118", "119", "120" ]
[ "nonn" ]
10
1
2
[ "A383192", "A383193", "A383194" ]
null
Yifan Xie, Apr 20 2025
2025-04-29T13:19:41
oeisdata/seq/A383/A383193.seq
0602eeee00392591983b1207f03160f8
A383194
The least number of times that b(k) = 2*k - 1 for the first n terms of a "mean-central" sequence, as is defined in A383192.
[ "1", "1", "2", "2", "3", "4", "4", "4", "4", "4", "5", "5", "6", "6", "6", "6", "7", "7", "7", "8", "8", "8", "9", "10", "10", "10", "10", "10", "11", "11" ]
[ "nonn", "more" ]
10
1
3
[ "A383192", "A383193", "A383194" ]
null
Yifan Xie, Apr 21 2025
2025-04-29T13:20:06
oeisdata/seq/A383/A383194.seq
c518d9e15753dbe8ca15f3ee9fb0b9d8
A383195
Primes that are the concatenation of three primes, of which two are equal.
[ "223", "227", "233", "277", "337", "353", "373", "557", "577", "727", "733", "757", "773", "1733", "1777", "1933", "2213", "2237", "2243", "2267", "2273", "2297", "2333", "2377", "3313", "3319", "3323", "3329", "3331", "3343", "3347", "3359", "3361", "3371", "3373", "3389", "3413", "3433", "3533", "3593", "3613", "3673", "3733", "3793", "3833", "4133", "4177", "4733", "5333", "5519", "5531", "5573" ]
[ "nonn" ]
20
1
1
[ "A100607", "A100633", "A383195" ]
null
Robert Israel, Apr 28 2025
2025-04-29T13:27:48
oeisdata/seq/A383/A383195.seq
69cd596ad62a9a72dacb117096eb30cb
A383196
Expansion of e.g.f. (1/(1 - 3*x)^(1/3) - 1)^3 / 6.
[ "0", "0", "0", "1", "24", "520", "11880", "295960", "8090880", "242280640", "7912262400", "280384720000", "10727852889600", "441104638374400", "19407654326860800", "910140650683264000", "45332366929833984000", "2390437704451084288000", "133060566042200788992000", "7797805996570952986624000" ]
[ "nonn" ]
10
0
5
[ "A001754", "A035119", "A143169", "A371080", "A383196" ]
null
Seiichi Manyama, Apr 19 2025
2025-05-03T03:00:05
oeisdata/seq/A383/A383196.seq
946645f4b3b4a1d3b822ef6d18ac2c36
A383197
Number of positive integers with n digits in which adjacent digits differ by at most 2.
[ "9", "41", "188", "867", "4010", "18574", "86096", "399225", "1851529", "8587802", "39833891", "184770640", "857073208", "3975623218", "18441391129", "85542653145", "396800342804", "1840608838251", "8537899488042", "39604141848678", "183708898915088", "852157340908409", "3952841397780937", "18335763176322738" ]
[ "nonn", "base", "easy" ]
17
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-04-23T13:10:04
oeisdata/seq/A383/A383197.seq
e856289de176059c5a15c6c52f9dc61d
A383198
Number of positive integers with n digits in which adjacent digits differ by at most 3.
[ "9", "54", "328", "2000", "12202", "74458", "454366", "2772710", "16920138", "103253214", "630091042", "3845059318", "23464039746", "143186649814", "873780342786", "5332145758694", "32538816680050", "198564450196598", "1211717109125762", "7394366670845606", "45123286657530514", "275359755529253142" ]
[ "nonn", "base", "easy" ]
13
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-05-02T10:32:51
oeisdata/seq/A383/A383198.seq
32e4092db2a8926ec423d82088f36271
A383199
Number of positive integers with n digits in which adjacent digits differ by at most 4.
[ "9", "65", "475", "3465", "25282", "184463", "1345887", "9819916", "71648478", "522764591", "3814216651", "27829445433", "203050351876", "1481504383412", "10809413614854", "78868091114176", "575440631436879", "4198553757680021", "30633661742154286", "223510591001999469", "1630787227154056312" ]
[ "nonn", "base", "easy" ]
15
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-05-02T10:33:14
oeisdata/seq/A383/A383199.seq
17f7671c25313b5cbd2228da9ee8e909
A383200
Number of positive integers with n digits in which adjacent digits differ by at most 5.
[ "9", "74", "610", "5020", "41317", "340050", "2798709", "23034169", "189577752", "1560278726", "12841536934", "105689495131", "869854553902", "7159149960981", "58921836913893", "484943447787706", "3991222267830858", "32848892512931768", "270355712339865433", "2225104276073281126", "18313239977617203949" ]
[ "nonn", "base", "easy" ]
17
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-05-08T09:59:21
oeisdata/seq/A383/A383200.seq
137f4e1712671a3e74cf5ff58582d52a
A383201
Number of positive integers with n digits in which adjacent digits differ by at most 6.
[ "9", "81", "724", "6472", "57851", "517112", "4622299", "41317257", "369321783", "3301249634", "29508817638", "263769909867", "2357755102376", "21075220921085", "188384678470177", "1683910560899833", "15051939468415328", "134544486519385896", "1202650255852445247", "10750107085908359068" ]
[ "nonn", "base", "easy" ]
14
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-05-02T17:13:08
oeisdata/seq/A383/A383201.seq
9b50d26590c3a12033a4d69afa7112fa
A383202
Number of positive integers with n digits in which adjacent digits differ by at most 7.
[ "9", "86", "813", "7693", "72786", "688661", "6515721", "61648078", "583279341", "5518660133", "52214449434", "494023669525", "4674173312097", "44224391459894", "418426247682381", "3958913146568317", "37457003208767394", "354397037125653845", "3353104871295311673", "31725187008033469918" ]
[ "nonn", "base", "easy" ]
16
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-05-07T20:05:24
oeisdata/seq/A383/A383202.seq
472be38d7fab701ea5ec24646fde6c9c
A383203
Expansion of e.g.f. f(x) * exp(f(x)), where f(x) = (exp(2*x) - 1)/2.
[ "0", "1", "4", "19", "104", "641", "4380", "32803", "266768", "2337505", "21925236", "218946003", "2316939256", "25878593313", "304020964876", "3745210267939", "48248600421664", "648460085178689", "9072650530778084", "131884007007981075", "1988341404357799048", "31040812899065995073", "501049583881525932028" ]
[ "nonn" ]
9
0
3
[ "A154602", "A383203" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:05:04
oeisdata/seq/A383/A383203.seq
c49ae1682bd6228ac928f91e0de32a6c
A383204
Expansion of e.g.f. f(x)^2 * exp(f(x)) / 2, where f(x) = (exp(2*x) - 1)/2.
[ "0", "0", "1", "9", "70", "550", "4531", "39515", "365324", "3575820", "36971461", "402741581", "4610187154", "55316069874", "694067320311", "9087012399007", "123889735839000", "1755654433460248", "25816120675972105", "393285627390135313", "6198118449550830302", "100916786871955767998", "1695424878199285059003" ]
[ "nonn" ]
7
0
4
[ "A154602", "A383204" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:04:10
oeisdata/seq/A383/A383204.seq
a8fe307973b64a2315620ed281cbfef8
A383205
Expansion of e.g.f. f(x)^3 * exp(f(x)) / 6, where f(x) = (exp(2*x) - 1)/2.
[ "0", "0", "0", "1", "16", "190", "2080", "22491", "247072", "2792476", "32659840", "396255541", "4991365808", "65268062938", "885442472096", "12451577262671", "181326192307264", "2731564737248696", "42522062246582784", "683301050932028777", "11322975536640636240", "193300021823406703990", "3396381539718451143200" ]
[ "nonn" ]
7
0
5
[ "A154602", "A383205" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:03:29
oeisdata/seq/A383/A383205.seq
3fb25b2d0d13b39ad80854f9bef3d100
A383206
Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) = Sum_{j=k..n} 2^(n-j) * Stirling2(n,j) * Stirling2(j,k).
[ "1", "0", "1", "0", "3", "1", "0", "11", "9", "1", "0", "49", "71", "18", "1", "0", "257", "575", "245", "30", "1", "0", "1539", "4957", "3120", "625", "45", "1", "0", "10299", "45829", "39697", "11480", "1330", "63", "1", "0", "75905", "454015", "517790", "201677", "33250", "2506", "84", "1", "0", "609441", "4804191", "6999785", "3513762", "770007", "81774", "4326", "108", "1" ]
[ "nonn", "tabl" ]
11
0
5
[ "A000007", "A004211", "A130191", "A380228", "A383206", "A383207", "A383208" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:04:05
oeisdata/seq/A383/A383206.seq
8ed4401044675307e47ee117edf1b4f8
A383207
Expansion of e.g.f. (exp(f(x)) - 1)^2 / 2, where f(x) = (exp(2*x) - 1)/2.
[ "0", "0", "1", "9", "71", "575", "4957", "45829", "454015", "4804191", "54094749", "645720757", "8142419727", "108110708511", "1506969153757", "21993472779461", "335257957315199", "5325979566073919", "87999598425114045", "1509471498829147637", "26835040585117438415", "493677094649876461759", "9384926300821643459133" ]
[ "nonn" ]
9
0
4
[ "A000558", "A383206", "A383207" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:04:14
oeisdata/seq/A383/A383207.seq
e7fcd2affd63c9a47667e76e34beb0cc
A383208
Expansion of e.g.f. (exp(f(x)) - 1)^3 / 6, where f(x) = (exp(2*x) - 1)/2.
[ "0", "0", "0", "1", "18", "245", "3120", "39697", "517790", "6999785", "98520060", "1445923149", "22129416210", "352932509085", "5859167661256", "101122879922313", "1811960841148774", "33662625853200337", "647550189266734452", "12881675626292023173", "264677402162135670554", "5610552395871699336453" ]
[ "nonn" ]
8
0
5
[ "A000559", "A383206", "A383208" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:04:18
oeisdata/seq/A383/A383208.seq
42b9cd1f90f8f8ac1f9478263e5227dd
A383209
Irregular triangle read by rows in which row n lists the odd divisors m of n such that there is a divisor d of n with d < m < 2*d, or 0 if such odd divisors do not exist.
[ "0", "0", "0", "0", "0", "3", "0", "0", "0", "0", "0", "3", "0", "0", "5", "0", "0", "3", "9", "0", "5", "0", "0", "0", "3", "0", "0", "0", "7", "0", "3", "5", "15", "0", "0", "0", "0", "7", "3", "9", "0", "0", "0", "5", "0", "3", "7", "21", "0", "0", "5", "9", "15", "0", "0", "3", "0", "0", "0", "0", "0", "3", "9", "27", "0", "7", "0", "0", "0", "3", "5", "15", "0", "0", "9", "0", "0", "3", "11", "33", "0", "0", "0", "7", "0", "3", "9", "0", "0", "5", "25", "0", "11", "3", "39" ]
[ "nonn", "tabf" ]
26
1
6
[ "A027750", "A237593", "A239657", "A379288", "A379374", "A379461", "A383147", "A383209" ]
null
Omar E. Pol, Apr 19 2025
2025-04-27T15:06:20
oeisdata/seq/A383/A383209.seq
ad300f36a49904cc8b08793eac17ebcf
A383210
The Dirichlet inverse of A382883.
[ "1", "1", "1", "0", "1", "1", "1", "-2", "0", "1", "1", "-1", "1", "1", "1", "-3", "1", "-1", "1", "-1", "1", "1", "1", "-5", "0", "1", "-2", "-1", "1", "1", "1", "-2", "1", "1", "1", "-2", "1", "1", "1", "-5", "1", "1", "1", "-1", "-1", "1", "1", "-6", "0", "-1", "1", "-1", "1", "-5", "1", "-5", "1", "1", "1", "-3", "1", "1", "-1", "3", "1", "1", "1", "-1", "1", "1", "1", "-2", "1", "1", "-1", "-1", "1", "1", "1" ]
[ "sign" ]
10
1
8
[ "A382883", "A383210" ]
null
Peter Luschny, Apr 19 2025
2025-04-29T16:51:58
oeisdata/seq/A383/A383210.seq
812be7e3c933557cd16496bb7acdb777
A383211
Numbers of the form p^e where p is prime and e > 1 is squarefree.
[ "4", "8", "9", "25", "27", "32", "49", "64", "121", "125", "128", "169", "243", "289", "343", "361", "529", "729", "841", "961", "1024", "1331", "1369", "1681", "1849", "2048", "2187", "2197", "2209", "2809", "3125", "3481", "3721", "4489", "4913", "5041", "5329", "6241", "6859", "6889", "7921", "8192", "9409", "10201", "10609", "11449", "11881", "12167" ]
[ "nonn" ]
24
1
1
[ "A005117", "A053810", "A144338", "A383211", "A383266" ]
null
Peter Luschny, Apr 21 2025
2025-05-28T14:19:37
oeisdata/seq/A383/A383211.seq
6560de0fa2795d447a79ff6bea5b6a51
A383212
a(n) = permanent of the n-th principal submatrix of the rectangular array whose odd-numbered rows are (2,1,2,1,2,1,2,1,...) and even-numbered rows are (1,2,1,2,1,2,1,2,...).
[ "1", "2", "5", "24", "132", "1032", "8820", "95616", "1106496", "15327360", "223560000", "3768768000", "66305952000", "1316927808000", "27127003680000", "620221722624000", "14638710417408000", "378633583448064000", "10073602372700160000", "290788929384726528000", "8609476463579013120000", "274361332654900592640000", "8946658680536444313600000" ]
[ "nonn" ]
18
0
2
[ "A204252", "A383212" ]
null
Clark Kimberling, Apr 19 2025
2025-04-24T09:01:55
oeisdata/seq/A383/A383212.seq
c12989626deb51f74e06eb3791df90f1
A383213
a(n) = number of distinct prime factors of binomial(2n,n+1).
[ "0", "1", "2", "2", "4", "3", "4", "4", "5", "5", "6", "6", "6", "7", "6", "7", "9", "8", "10", "9", "10", "10", "10", "9", "10", "10", "11", "11", "12", "13", "12", "12", "14", "14", "14", "14", "14", "14", "16", "14", "16", "15", "16", "17", "16", "17", "18", "17", "18", "18", "18", "18", "20", "18", "20", "19", "19", "20", "20", "21", "21", "21", "21", "21", "23", "22", "24", "23", "23", "23" ]
[ "nonn" ]
20
1
3
[ "A000984", "A001221", "A067434", "A383213", "A383214" ]
null
Clark Kimberling, Apr 19 2025
2025-04-26T20:30:09
oeisdata/seq/A383/A383213.seq
a5e9be5f4d029c480002c4b25313488c
A383214
a(n) = A067434(n) - A383213(n).
[ "1", "1", "0", "1", "-1", "1", "0", "1", "0", "0", "0", "0", "0", "-1", "1", "1", "-1", "1", "-1", "1", "0", "0", "-1", "1", "0", "0", "-1", "1", "1", "-1", "0", "1", "0", "0", "0", "0", "0", "1", "-2", "1", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "0", "0", "0", "-1", "2", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "1", "0", "0", "0", "0", "-1", "1", "0", "-1", "1", "-1", "1", "0", "-1", "1" ]
[ "sign" ]
8
1
39
[ "A000984", "A067634", "A383213", "A383214" ]
null
Clark Kimberling, Apr 19 2025
2025-05-03T17:45:24
oeisdata/seq/A383/A383214.seq
a3404b6e7488734b792e05fbca2e176c
A383215
Primes p preceded and followed by gaps whose difference (absolute value) is greater than log(p).
[ "7", "29", "31", "113", "127", "139", "149", "181", "191", "199", "223", "241", "283", "307", "317", "331", "347", "419", "421", "431", "467", "521", "523", "541", "619", "641", "661", "673", "773", "809", "811", "821", "829", "853", "863", "877", "887", "907", "953", "967", "1009", "1021", "1031", "1049", "1051", "1061", "1069", "1087", "1129", "1151", "1153", "1213", "1259", "1277" ]
[ "nonn" ]
22
1
1
[ "A036263", "A068985", "A383215", "A383216" ]
null
Alain Rocchelli, Apr 19 2025
2025-05-10T03:07:55
oeisdata/seq/A383/A383215.seq
60386ac0af9039d53e1882e9986d28b0
A383216
Primes p which are preceded and followed by gaps whose difference is greater than 2*log(p).
[ "113", "127", "523", "887", "907", "1087", "1129", "1151", "1277", "1327", "1361", "1669", "1693", "1931", "1951", "1973", "2203", "2311", "2333", "2477", "2557", "2971", "2999", "3163", "3251", "3299", "3469", "4049", "4297", "4327", "4523", "4547", "4783", "4861", "5119", "5147", "5237", "5351", "5381", "5531", "5557", "5591", "5749", "5779", "5981" ]
[ "nonn" ]
19
1
1
[ "A036263", "A092553", "A383215", "A383216" ]
null
Alain Rocchelli, Apr 19 2025
2025-05-10T03:07:50
oeisdata/seq/A383/A383216.seq
2434f21558d159bc2897de811ba79d70