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
2025-07-14 02:38:35
filename
stringlengths
29
29
hash
stringlengths
32
32
A363101
Even numbers that are neither prime powers nor squarefree.
[ "12", "18", "20", "24", "28", "36", "40", "44", "48", "50", "52", "54", "56", "60", "68", "72", "76", "80", "84", "88", "90", "92", "96", "98", "100", "104", "108", "112", "116", "120", "124", "126", "132", "136", "140", "144", "148", "150", "152", "156", "160", "162", "164", "168", "172", "176", "180", "184", "188", "192", "196", "198", "200", "204", "208", "212", "216", "220", "224", "228", "232", "234", "236", "240", "242" ]
[ "nonn" ]
11
1
1
[ "A001221", "A001222", "A005418", "A013929", "A024619", "A126706", "A177712", "A360769", "A363101" ]
null
Michael De Vlieger, May 19 2023
2023-10-27T16:38:46
oeisdata/seq/A363/A363101.seq
565b42fedc39f6e3d1b34ee4b5ccaf07
A363102
Denominator of the continued fraction 1/(2-3/(3-4/(4-5/(...(n-1)-n/(-2))))).
[ "7", "7", "23", "17", "47", "31", "79", "7", "17", "71", "167", "97", "223", "127", "41", "23", "359", "199", "439", "241", "31", "41", "89", "337", "727", "1", "839", "449", "137", "73", "1087", "577", "1223", "647", "1367", "103", "1", "47", "73", "881", "1847", "967", "1", "151", "2207", "1151", "2399", "1249", "113", "193", "401", "1", "3023", "1567", "191", "41", "71", "257", "3719", "113", "3967", "89", "103", "311" ]
[ "nonn" ]
43
3
1
[ "A008865", "A051403", "A059772", "A164314", "A356247", "A357127", "A363102" ]
null
Mohammed Bouras, May 19 2023
2024-08-06T22:00:31
oeisdata/seq/A363/A363102.seq
3fc3034a9c954cd8b0a6612da87aa584
A363103
Expansion of g.f. A(x) satisfying 1/3 = Sum_{n=-oo..+oo} x^n * (2*A(x) + (-x)^n)^(3*n-1).
[ "1", "18", "990", "76437", "6821604", "662170986", "67898785806", "7236062780346", "793535687872488", "88963928271478008", "10150301461460395149", "1174747280984088520626", "137580020162886643530525", "16274396085743934046292733", "1941610878042595564951651347", "233359133706492695158857170850" ]
[ "nonn" ]
8
0
2
null
null
Paul D. Hanna, May 18 2023
2023-05-18T10:41:12
oeisdata/seq/A363/A363103.seq
6611611889a454c9ee770b7b9bb23984
A363104
Expansion of g.f. A(x) satisfying 4 = Sum_{n=-oo..+oo} (-x)^n * (4*A(x) + x^(n-1))^(n+1).
[ "1", "6", "44", "348", "2886", "24800", "218888", "1972572", "18075100", "167900506", "1577467760", "14963979584", "143124912880", "1378756186748", "13365212659144", "130274948580864", "1276075285222662", "12554452588117632", "124003727286837484", "1229203475053859456", "12224294019862383720" ]
[ "nonn" ]
12
0
2
[ "A359670", "A359711", "A359712", "A359713", "A363104", "A363105", "A363184" ]
null
Paul D. Hanna, May 21 2023
2023-05-22T08:57:27
oeisdata/seq/A363/A363104.seq
103c8a89970acb5a7deee2ed4a97d6e0
A363105
Expansion of g.f. A(x) satisfying 5 = Sum_{n=-oo..+oo} (-x)^n * (5*A(x) + x^(n-1))^(n+1).
[ "1", "7", "59", "538", "5149", "51059", "520035", "5407889", "57181230", "612910369", "6644662132", "72731584789", "802696690614", "8922392225233", "99798739026795", "1122441028044882", "12686176392341722", "144013323190860339", "1641303449002365323", "18772674107796041770", "215413772477355781876" ]
[ "nonn" ]
7
0
2
[ "A359670", "A359711", "A359712", "A359713", "A363104", "A363105", "A363185" ]
null
Paul D. Hanna, May 21 2023
2023-05-22T08:57:22
oeisdata/seq/A363/A363105.seq
adf47ab735ee25edaf8095bec140d0ae
A363106
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n) * (A(x) + x^(n-2))^(n+1).
[ "1", "2", "5", "14", "36", "98", "271", "752", "2124", "6052", "17375", "50292", "146469", "428992", "1262946", "3734748", "11089366", "33048498", "98819841", "296388284", "891436452", "2688029716", "8124678435", "24611028218", "74702698749", "227177047220", "692084278902", "2111883982538", "6454350205098", "19754469483978" ]
[ "nonn" ]
9
0
2
[ "A359711", "A363106", "A363107", "A363108", "A363109", "A363140" ]
null
Paul D. Hanna, May 24 2023
2023-05-25T08:58:23
oeisdata/seq/A363/A363106.seq
06376156324bd74f5e629d87ef42bca8
A363107
Expansion of g.f. A(x) satisfying 2 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n) * (2*A(x) + x^(n-2))^(n+1).
[ "1", "2", "6", "20", "60", "196", "644", "2128", "7178", "24374", "83496", "288420", "1002272", "3503748", "12311818", "43458316", "154038006", "548018604", "1956263020", "7004845080", "25153186956", "90554989440", "326790211458", "1181910952584", "4283416505940", "15553332981066", "56575492155764", "206136324338908" ]
[ "nonn" ]
8
0
2
[ "A359712", "A363106", "A363107", "A363108", "A363109" ]
null
Paul D. Hanna, May 24 2023
2023-05-25T08:58:26
oeisdata/seq/A363/A363107.seq
99d3dece84e09467a054ba39e36b5742
A363108
Expansion of g.f. A(x) satisfying 3 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n) * (3*A(x) + x^(n-2))^(n+1).
[ "1", "2", "7", "26", "86", "318", "1165", "4312", "16318", "62020", "238165", "921980", "3590145", "14067188", "55399442", "219172028", "870736366", "3472155062", "13892694747", "55759406580", "224427809830", "905659181212", "3663475842865", "14851965523630", "60334690089827", "245572722474460", "1001306332164918" ]
[ "nonn" ]
10
0
2
[ "A359713", "A363106", "A363107", "A363108", "A363109" ]
null
Paul D. Hanna, May 24 2023
2023-05-25T08:58:29
oeisdata/seq/A363/A363108.seq
f9d9645ac9416335c73d7bae938b9f94
A363109
Expansion of g.f. A(x) satisfying 4 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n) * (4*A(x) + x^(n-2))^(n+1).
[ "1", "2", "8", "32", "114", "464", "1840", "7424", "30624", "126610", "529832", "2233584", "9471888", "40427152", "173398644", "747197976", "3233336302", "14043404136", "61203859260", "267565075736", "1173030487248", "5156102021680", "22718268675276", "100321210527344", "443919440641296", "1968097221659546" ]
[ "nonn" ]
10
0
2
[ "A363104", "A363106", "A363107", "A363108", "A363109" ]
null
Paul D. Hanna, May 24 2023
2023-05-25T08:58:33
oeisdata/seq/A363/A363109.seq
04316ed4e9da77827ccfdd97043c45d0
A363110
G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (k + (n-k+1)*x) / (1 + k*x + (n-k+1)*x^2).
[ "1", "1", "2", "4", "10", "28", "88", "306", "1158", "4730", "20722", "96776", "479340", "2507510", "13804014", "79718782", "481614806", "3036358968", "19932689952", "135981543762", "962319171782", "7053068549250", "53458038451082", "418440466421960", "3378290373259300", "28099682071640734", "240537280709926718" ]
[ "nonn" ]
16
0
3
[ "A067948", "A204064", "A204066", "A316370", "A363110" ]
null
Paul D. Hanna, Jun 02 2023
2023-06-09T09:14:37
oeisdata/seq/A363/A363110.seq
8facb9f190f1bf37e770ae14c5423483
A363111
Expansion of g.f. A(x) = F(x*F(x)^7), where F(x) = 1 + x*F(x)^4 is the g.f. of A002293.
[ "1", "1", "11", "127", "1547", "19652", "258069", "3481034", "47999915", "674086924", "9612919156", "138878011335", "2028718584989", "29918897595468", "444889269572286", "6663228661354420", "100430376524360459", "1522215623202615036", "23187346871707554564", "354783440893854307244" ]
[ "nonn" ]
9
0
3
[ "A002293", "A363111", "A363304", "A363308", "A363309" ]
null
Paul D. Hanna, May 30 2023
2023-05-31T09:07:40
oeisdata/seq/A363/A363111.seq
7dd6f53768795d1b1e14e81af0ae2939
A363112
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - x^n)^(2*n-1).
[ "1", "1", "6", "51", "470", "4716", "49350", "534115", "5929892", "67175779", "773473709", "9025907984", "106511693025", "1268898400188", "15240421643846", "184348620664449", "2243749948233175", "27459089491691552", "337685454820968084", "4170918486201555250", "51719670553572755173", "643610071084847351183" ]
[ "nonn" ]
9
0
3
[ "A357227", "A361772", "A363112", "A363113", "A363114" ]
null
Paul D. Hanna, May 14 2023
2023-05-16T04:22:05
oeisdata/seq/A363/A363112.seq
1809d06875c399cebbf41ad8a376e5f3
A363113
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - x^n)^(3*n-1).
[ "1", "2", "30", "621", "14196", "351802", "9179386", "248533626", "6917835992", "196730606200", "5691264122213", "166961281712818", "4955321842136163", "148522859439511133", "4489164688548477495", "136677755757518772050", "4187859771944659634378", "129039023692329781903247", "3995878021838502688832856" ]
[ "nonn" ]
9
0
2
[ "A357227", "A361773", "A363112", "A363113", "A363114" ]
null
Paul D. Hanna, May 14 2023
2023-05-15T08:46:51
oeisdata/seq/A363/A363113.seq
11ad8b8aa835f294df79020183bf6bfd
A363114
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - x^n)^(4*n-1).
[ "1", "4", "138", "6571", "353935", "20694945", "1276853497", "81834405039", "5395444806588", "363600236084796", "24933767742193052", "1734273108108910743", "122058422998192278797", "8676376795137864622232", "622018188741046650309066", "44922343315319150402783783", "3265215115112327274815579250" ]
[ "nonn" ]
5
0
2
[ "A357227", "A361774", "A363112", "A363113", "A363114" ]
null
Paul D. Hanna, May 14 2023
2023-05-15T08:46:57
oeisdata/seq/A363/A363114.seq
a086d37898e4a1450ba53a820869ed78
A363115
Expansion of e.g.f. log(1 - log( sqrt(1-2*x) )).
[ "0", "1", "1", "4", "22", "168", "1616", "18800", "256432", "4012288", "70825344", "1392214272", "30157260288", "713680180224", "18319344307200", "506934586748928", "15043324048398336", "476540007615725568", "16050059458251915264", "572710950848334200832", "21582629580640554123264", "856552661738538476765184" ]
[ "nonn" ]
5
0
4
[ "A003713", "A089064", "A363115", "A363116" ]
null
Paul D. Hanna, Jun 09 2023
2023-06-09T08:44:30
oeisdata/seq/A363/A363115.seq
ee6416534a941d7fd81b00ff60541c2e
A363116
Expansion of e.g.f. log(1 - (1/3)*log(1-3*x)).
[ "0", "1", "2", "11", "93", "1068", "15486", "271206", "5566086", "130982328", "3476230344", "102709363392", "3343387479840", "118880973126576", "4584247231485312", "190548125567321328", "8492669888285758896", "404023626910206388224", "20434095445804056842112", "1094849162137482139541376" ]
[ "nonn" ]
5
0
3
[ "A003713", "A089064", "A363115", "A363116" ]
null
Paul D. Hanna, Jun 09 2023
2023-06-09T08:44:04
oeisdata/seq/A363/A363116.seq
f2a91965b01a7e13889c8bc1e78296dc
A363117
Decimal expansion of Product_{k>=1} (1 - exp(-7*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "7", "1", "8", "5", "7", "3", "1", "5", "4", "1", "7", "2", "2", "4", "3", "6", "5", "8", "3", "8", "2", "9", "0", "1", "2", "3", "6", "4", "6", "2", "9", "1", "9", "5", "6", "0", "2", "5", "7", "0", "7", "6", "4", "9", "0", "2", "9", "8", "1", "2", "2", "0", "8", "6", "1", "0", "0", "1", "1", "7", "6", "6", "9", "4", "5", "4", "3", "5", "0", "1", "4", "7", "6", "7", "0", "9", "9", "1", "9", "7", "6", "5", "2", "7", "6", "7", "7", "8", "9", "3", "4", "4", "1", "7", "5", "6", "3" ]
[ "nonn", "cons" ]
10
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 15 2023
2023-05-19T14:31:08
oeisdata/seq/A363/A363117.seq
42727ea0d2519765525f8f18c34eaf9e
A363118
Decimal expansion of Product_{k>=1} (1 - exp(-9*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "4", "7", "4", "4", "5", "1", "4", "8", "2", "3", "9", "9", "0", "7", "8", "9", "4", "3", "2", "3", "3", "3", "9", "4", "9", "2", "8", "7", "9", "7", "1", "6", "4", "4", "0", "0", "5", "2", "7", "5", "1", "3", "4", "3", "8", "8", "1", "9", "8", "7", "3", "9", "1", "8", "2", "6", "0", "6", "6", "0", "2", "4", "0", "5", "6", "1", "9", "2", "1", "1", "3", "2", "7", "4", "3", "6", "9", "7", "0", "9", "0", "8", "3", "8", "4", "0", "0", "8", "2", "7", "2", "0", "3", "0" ]
[ "nonn", "cons" ]
9
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 15 2023
2023-05-19T14:31:36
oeisdata/seq/A363/A363118.seq
83ad21c5271ce7dc2afd4b6642b1f4bd
A363119
Decimal expansion of Product_{k>=1} (1 - exp(-14*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "2", "0", "7", "9", "8", "9", "3", "0", "4", "9", "2", "0", "1", "8", "8", "7", "7", "3", "5", "7", "8", "2", "1", "2", "4", "8", "3", "6", "1", "1", "1", "5", "7", "9", "6", "8", "4", "9", "9", "8", "0", "3", "8", "4", "1", "1", "0", "8", "1", "1", "1", "3", "1", "5", "0", "8", "1", "3", "3", "4", "4", "1", "9", "1", "3", "7", "5", "6", "3", "4", "7", "6", "7", "2", "4", "9", "8", "5", "6", "5", "1", "3", "8", "9", "7", "0", "8" ]
[ "nonn", "cons" ]
10
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 15 2023
2023-05-19T14:32:32
oeisdata/seq/A363/A363119.seq
6620a89af9c3c2a4bcf7aa3be02198a1
A363120
Decimal expansion of Product_{k>=1} (1 - exp(-18*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "7", "2", "3", "7", "9", "8", "7", "5", "5", "6", "4", "7", "7", "6", "4", "6", "8", "4", "5", "1", "2", "4", "2", "7", "2", "0", "4", "4", "4", "8", "2", "4", "4", "3", "6", "6", "1", "8", "8", "1", "9", "7", "0", "8", "7", "1", "6", "5", "9", "0", "2", "5", "6", "0", "8", "6", "2", "5", "8", "9", "3", "9", "4", "7", "0", "4", "7", "9", "0", "6", "5", "8", "4", "0", "2", "2", "2", "1", "2", "8", "2", "9" ]
[ "nonn", "cons" ]
10
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 15 2023
2023-05-19T14:32:48
oeisdata/seq/A363/A363120.seq
2ed2ca6061660386a73799bc7ada6bf4
A363121
Primitive terms of A116882: terms k of A116882 such that k/2 is not a term of A116882.
[ "1", "12", "40", "56", "144", "176", "208", "240", "544", "608", "672", "736", "800", "864", "928", "992", "2112", "2240", "2368", "2496", "2624", "2752", "2880", "3008", "3136", "3264", "3392", "3520", "3648", "3776", "3904", "4032", "8320", "8576", "8832", "9088", "9344", "9600", "9856", "10112", "10368", "10624", "10880", "11136", "11392", "11648", "11904" ]
[ "nonn", "easy" ]
19
1
2
[ "A070941", "A116882", "A363121" ]
null
Amiram Eldar, May 16 2023
2023-05-18T10:40:27
oeisdata/seq/A363/A363121.seq
21dec46908d77f681cc050e41f3f2bac
A363122
Numbers k such that the highest power of 2 dividing k is larger than the highest power of p dividing k for any odd prime p.
[ "2", "4", "8", "12", "16", "24", "32", "40", "48", "56", "64", "80", "96", "112", "120", "128", "144", "160", "168", "176", "192", "208", "224", "240", "256", "280", "288", "320", "336", "352", "384", "416", "448", "480", "512", "528", "544", "560", "576", "608", "624", "640", "672", "704", "720", "736", "768", "800", "832", "840", "864", "880", "896", "928", "960", "992" ]
[ "nonn", "easy" ]
16
1
1
[ "A006519", "A034699", "A116882", "A174973", "A363122", "A363123" ]
null
Amiram Eldar, May 16 2023
2023-10-04T06:49:05
oeisdata/seq/A363/A363122.seq
953f587cb9fe689f61dd096453261a61
A363123
Primitive terms of A363122: terms k of A363122 such that k/2 is not a term of A363122.
[ "2", "12", "40", "56", "120", "144", "168", "176", "208", "280", "528", "544", "608", "624", "720", "736", "800", "840", "864", "880", "928", "992", "1008", "1040", "1232", "1456", "1584", "1632", "1824", "1872", "2208", "2288", "2368", "2400", "2624", "2640", "2720", "2752", "2784", "2976", "3008", "3040", "3120", "3136", "3392", "3680", "3696", "3776" ]
[ "nonn", "easy" ]
20
1
1
[ "A363122", "A363123" ]
null
Amiram Eldar, May 16 2023
2023-05-19T04:23:46
oeisdata/seq/A363/A363123.seq
6b73f628001f4047a354f1560218dabd
A363124
Number of integer partitions of n with more than one non-mode.
[ "0", "0", "0", "0", "0", "0", "0", "1", "3", "6", "9", "19", "28", "46", "65", "98", "132", "190", "251", "348", "451", "603", "768", "1014", "1273", "1648", "2052", "2604", "3233", "4062", "4984", "6203", "7582", "9333", "11349", "13890", "16763", "20388", "24528", "29613", "35502", "42660", "50880", "60883", "72376", "86158", "102120", "121133", "143010" ]
[ "nonn" ]
9
0
9
[ "A000041", "A002865", "A008284", "A053263", "A058398", "A098859", "A237984", "A238478", "A238479", "A275870", "A327472", "A353836", "A353863", "A359893", "A362607", "A362608", "A362609", "A362610", "A362611", "A362612", "A362614", "A363124", "A363125", "A363126", "A363127", "A363128", "A363129" ]
null
Gus Wiseman, May 16 2023
2023-05-17T08:35:59
oeisdata/seq/A363/A363124.seq
7792e69b213fd4bbdccaafca51cc3ab8
A363125
Number of integer partitions of n with a unique non-mode.
[ "0", "0", "0", "0", "1", "3", "3", "8", "9", "13", "18", "24", "24", "36", "41", "45", "57", "68", "72", "87", "95", "105", "131", "136", "149", "164", "199", "203", "232", "246", "276", "298", "335", "347", "409", "399", "467", "488", "567", "569", "636", "662", "757", "767", "878", "887", "1028", "1030", "1168", "1181", "1342", "1388", "1558", "1570", "1789", "1791" ]
[ "nonn" ]
6
0
6
[ "A000041", "A002865", "A008284", "A053263", "A058398", "A098859", "A237984", "A238478", "A238479", "A275870", "A327472", "A353836", "A353863", "A359893", "A362607", "A362608", "A362609", "A362610", "A362611", "A362612", "A362614", "A363124", "A363125", "A363126", "A363127", "A363128", "A363129" ]
null
Gus Wiseman, May 16 2023
2023-05-17T08:35:54
oeisdata/seq/A363/A363125.seq
10ef2136aa4ca25824e5642a5f4a617b
A363126
Irregular triangle read by rows where T(n,k) is the number of integer partitions of n with k non-modes, all 0's removed.
[ "1", "1", "2", "3", "4", "1", "4", "3", "8", "3", "6", "8", "1", "10", "9", "3", "11", "13", "6", "15", "18", "9", "13", "24", "18", "1", "25", "24", "25", "3", "19", "36", "40", "6", "29", "41", "52", "13", "33", "45", "79", "19", "42", "57", "95", "36", "1", "39", "68", "133", "54", "3", "62", "72", "158", "87", "6", "55", "87", "214", "121", "13", "81", "95", "250", "177", "24" ]
[ "nonn", "tabf" ]
6
0
3
[ "A000041", "A000196", "A002865", "A008284", "A047966", "A053263", "A058398", "A098859", "A237984", "A238478", "A275870", "A327472", "A353836", "A353863", "A353864", "A359893", "A362611", "A362612", "A362613", "A362614", "A362615", "A363124", "A363125", "A363126", "A363127", "A363130", "A363131" ]
null
Gus Wiseman, May 16 2023
2023-05-17T23:25:55
oeisdata/seq/A363/A363126.seq
e8118853099dca69168ed9f1f76d2f92
A363127
Number of non-modes in the multiset of prime factors of n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "2", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "2", "0", "0", "0" ]
[ "nonn" ]
6
1
60
[ "A001221", "A001222", "A002865", "A027746", "A047966", "A051903", "A056239", "A072774", "A088860", "A112798", "A124010", "A353863", "A362611", "A362613", "A362614", "A362615", "A362616", "A363124", "A363125", "A363126", "A363127", "A363130", "A363131" ]
null
Gus Wiseman, May 16 2023
2023-05-17T23:25:51
oeisdata/seq/A363/A363127.seq
1334e9ba40c21bc3004d941055b2c8fb
A363128
Number of integer partitions of n with more than one non-co-mode.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "3", "6", "9", "18", "25", "44", "60", "96", "122", "188", "243", "344", "442", "615", "769", "1047", "1308", "1722", "2150", "2791", "3430", "4405", "5401", "6803", "8326", "10408", "12608", "15641", "18906", "23179", "27935", "34061", "40778", "49451", "59038", "71060", "84604", "101386", "120114", "143358" ]
[ "nonn" ]
6
0
11
[ "A000041", "A002865", "A008284", "A053263", "A058398", "A098859", "A237984", "A238478", "A238479", "A275870", "A327472", "A353836", "A353863", "A359893", "A362607", "A362608", "A362609", "A362610", "A362611", "A362612", "A362613", "A362614", "A362615", "A363124", "A363125", "A363126", "A363127", "A363128", "A363129", "A363130", "A363131" ]
null
Gus Wiseman, May 18 2023
2023-05-18T08:33:30
oeisdata/seq/A363/A363128.seq
729939eb855c11e1c4ba711b0d10dcf7
A363129
Number of integer partitions of n with a unique non-co-mode.
[ "0", "0", "0", "0", "1", "3", "3", "9", "12", "18", "24", "37", "43", "64", "81", "99", "129", "162", "201", "247", "303", "364", "457", "535", "653", "765", "943", "1085", "1315", "1517", "1830", "2096", "2516", "2877", "3432", "3881", "4622", "5235", "6189", "7003", "8203", "9261", "10859", "12199", "14216", "15985", "18544", "20777", "24064", "26897" ]
[ "nonn" ]
5
0
6
[ "A000041", "A002133", "A002865", "A008284", "A053263", "A058398", "A098859", "A237984", "A238478", "A238479", "A275870", "A327472", "A353836", "A353863", "A359893", "A362607", "A362608", "A362609", "A362610", "A362611", "A362612", "A362613", "A362614", "A362615", "A363124", "A363125", "A363126", "A363127", "A363128", "A363129", "A363130", "A363131" ]
null
Gus Wiseman, May 18 2023
2023-05-18T08:34:52
oeisdata/seq/A363/A363129.seq
d24fc8aa725cf2003c6c9630daaa3769
A363130
Irregular triangle read by rows where T(n,k) is the number of integer partitions of n with k non-co-modes, all 0's removed.
[ "1", "1", "2", "3", "4", "1", "4", "3", "8", "3", "6", "9", "10", "12", "11", "18", "1", "15", "24", "3", "13", "37", "6", "25", "43", "9", "19", "64", "18", "29", "81", "25", "33", "99", "44", "42", "129", "59", "1", "39", "162", "93", "3", "62", "201", "116", "6", "55", "247", "175", "13", "81", "303", "224", "19", "84", "364", "309", "35", "103", "457", "389", "53", "105", "535", "529", "86" ]
[ "nonn", "tabf" ]
5
0
3
[ "A000041", "A000196", "A002865", "A008284", "A047966", "A053263", "A058398", "A098859", "A237984", "A275870", "A327472", "A353836", "A353863", "A359893", "A362611", "A362612", "A362613", "A362614", "A362615", "A363124", "A363125", "A363126", "A363127", "A363128", "A363129", "A363130", "A363131" ]
null
Gus Wiseman, May 18 2023
2023-05-18T08:33:26
oeisdata/seq/A363/A363130.seq
40692a022b69018ba2ebea405d82df0f
A363131
Number of non-co-modes in the prime factorization of n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0" ]
[ "nonn" ]
6
1
null
[ "A001221", "A001222", "A002865", "A027746", "A047966", "A051903", "A056239", "A059404", "A072774", "A098859", "A112798", "A124010", "A228593", "A237984", "A327472", "A353863", "A362611", "A362613", "A362614", "A362615", "A362616", "A362983", "A363126", "A363127", "A363128", "A363129", "A363130", "A363131" ]
null
Gus Wiseman, May 18 2023
2023-05-18T08:33:21
oeisdata/seq/A363/A363131.seq
651a7ba97e8b01d979f10a6c95b7cc48
A363132
Number of integer partitions of 2n such that 2*(minimum) = (mean).
[ "0", "0", "1", "2", "5", "6", "15", "14", "32", "34", "65", "55", "150", "100", "225", "237", "425", "296", "824", "489", "1267", "1133", "1809", "1254", "4018", "2142", "4499", "4550", "7939", "4564", "14571", "6841", "18285", "16047", "23408", "17495", "52545", "21636", "49943", "51182", "92516", "44582", "144872", "63260", "175318", "169232", "205353" ]
[ "nonn" ]
15
0
4
[ "A000009", "A000041", "A008284", "A051293", "A053263", "A058398", "A067538", "A099777", "A111907", "A118096", "A237753", "A237755", "A237757", "A237824", "A268192", "A326844", "A327482", "A349156", "A361851", "A361852", "A361853", "A361854", "A361855", "A361861", "A361906", "A361907", "A363132", "A363133", "A363134", "A363218", "A363224" ]
null
Gus Wiseman, May 23 2023
2023-12-30T21:24:01
oeisdata/seq/A363/A363132.seq
636c21385038cdcecdeaf8d4a640b488
A363133
Numbers > 1 whose prime indices satisfy 2*(minimum) = (mean).
[ "10", "28", "30", "39", "84", "88", "90", "100", "115", "171", "208", "252", "255", "259", "264", "270", "273", "280", "300", "363", "517", "544", "624", "756", "783", "784", "792", "793", "810", "840", "880", "900", "925", "1000", "1035", "1085", "1197", "1216", "1241", "1425", "1495", "1521", "1595", "1615", "1632", "1683", "1691", "1785", "1872", "1911" ]
[ "nonn" ]
6
1
1
[ "A000961", "A001222", "A006141", "A051293", "A056239", "A106529", "A111907", "A112798", "A118096", "A237753", "A237755", "A237757", "A237824", "A324522", "A327482", "A360005", "A361860", "A361861", "A361908", "A362050", "A363132", "A363133", "A363134", "A363218" ]
null
Gus Wiseman, May 29 2023
2023-05-31T10:48:35
oeisdata/seq/A363/A363133.seq
9720605c7db98754b1f8a8ef03abb075
A363134
Positive integers whose multiset of prime indices satisfies: (length) = 2*(minimum).
[ "4", "6", "10", "14", "22", "26", "34", "38", "46", "58", "62", "74", "81", "82", "86", "94", "106", "118", "122", "134", "135", "142", "146", "158", "166", "178", "189", "194", "202", "206", "214", "218", "225", "226", "254", "262", "274", "278", "297", "298", "302", "314", "315", "326", "334", "346", "351", "358", "362", "375", "382", "386", "394", "398", "422", "441" ]
[ "nonn" ]
5
1
1
[ "A000961", "A001222", "A006141", "A046660", "A051293", "A055396", "A056239", "A061395", "A106529", "A111907", "A112798", "A118096", "A237753", "A237755", "A237757", "A237824", "A324522", "A327482", "A360005", "A361860", "A361861", "A361908", "A362050", "A363132", "A363133", "A363134", "A363218" ]
null
Gus Wiseman, Jun 05 2023
2023-06-05T17:07:20
oeisdata/seq/A363/A363134.seq
dad17e4a8bbe68fc79e18dff243145f2
A363135
Expansion of g.f. A(x) satisfying A(x)^2 = Sum_{n=-oo..+oo} (-x)^n * (A(x)^3 + x^(n-1))^(n+1).
[ "1", "3", "17", "133", "1201", "11796", "122192", "1314266", "14536760", "164299909", "1889209112", "22030014333", "259903138431", "3096573445278", "37205465163246", "450292741602439", "5484622483791007", "67179073566189256", "826958737112517885", "10225081367973756189", "126936946636845618425" ]
[ "nonn" ]
10
0
2
[ "A359670", "A361770", "A363135", "A363136", "A363137" ]
null
Paul D. Hanna, May 26 2023
2023-05-26T16:49:07
oeisdata/seq/A363/A363135.seq
fc073e18a6d3b3ad0b56f11c3283d6e9
A363136
Expansion of g.f. A(x) satisfying A(x)^3 = Sum_{n=-oo..+oo} (-x)^n * (A(x)^4 + x^(n-1))^(n+1).
[ "1", "3", "20", "201", "2364", "30356", "412223", "5821790", "84640367", "1258323895", "19041449659", "292322012264", "4541588520144", "71272574697572", "1128153098245655", "17990251268286993", "288748431461195204", "4660994483707782316", "75619617951059214712", "1232402387922242020729" ]
[ "nonn" ]
9
0
2
[ "A359670", "A361770", "A363135", "A363136", "A363137" ]
null
Paul D. Hanna, May 26 2023
2023-05-26T16:49:29
oeisdata/seq/A363/A363136.seq
6ddfcf5cd6913283c7a9eb4df0f56842
A363137
Expansion of g.f. A(x) satisfying A(x)^4 = Sum_{n=-oo..+oo} (-x)^n * (A(x)^5 + x^(n-1))^(n+1).
[ "1", "3", "23", "284", "4125", "65526", "1102403", "19305377", "348217156", "6425056149", "120700893495", "2300815588583", "44391646154596", "865243089927133", "17011581975085968", "336981451741477122", "6719019528496352690", "134742110298875293027", "2715909284023948643846", "54992586234084937679092" ]
[ "nonn" ]
11
0
2
[ "A359670", "A361770", "A363135", "A363136", "A363137" ]
null
Paul D. Hanna, May 26 2023
2023-05-27T00:47:45
oeisdata/seq/A363/A363137.seq
9d55c38edcb27865b63552012afd75f2
A363138
G.f. A(x) satisfies: 0 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n) * (A(x) - x^n)^n * (1 - x^n*A(x))^n.
[ "1", "2", "4", "10", "32", "110", "380", "1452", "5444", "21422", "84348", "339498", "1375168", "5638930", "23273316", "96829410", "405119328", "1704806800", "7207449048", "30607173180", "130475372576", "558195492452", "2395675502344", "10312175675736", "44507875822784", "192575428797954", "835133872734696", "3629372408642778" ]
[ "nonn" ]
7
0
2
[ "A354963", "A363138" ]
null
Paul D. Hanna, Jun 12 2023
2023-06-13T08:04:14
oeisdata/seq/A363/A363138.seq
fc7cd4cb54bf23be6abbebdc908542af
A363139
Expansion of A(x) satisfying -x = Sum_{n=-oo..+oo} (-x)^n * (1 - (-x)^n)^n / A(x)^n.
[ "1", "1", "2", "3", "10", "29", "72", "190", "520", "1413", "3888", "10839", "30421", "86218", "246499", "708931", "2050584", "5962100", "17407554", "51019081", "150052163", "442677295", "1309668356", "3884884796", "11551622175", "34425468793", "102807253860", "307617338332", "922112808168", "2768808168311", "8327028966970" ]
[ "nonn" ]
9
0
3
[ "A357399", "A363139" ]
null
Paul D. Hanna, May 30 2023
2023-05-31T09:07:35
oeisdata/seq/A363/A363139.seq
92760e796402760ea02d22f1dd03730f
A363140
Expansion of g.f. A(x) satisfying 2 = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x) + x^(2*n))^(2*n+1).
[ "1", "2", "5", "20", "86", "396", "1887", "9277", "46748", "240189", "1253474", "6625814", "35401302", "190878795", "1037296173", "5675580349", "31240459117", "172871809365", "961124621229", "5366264076784", "30076030970681", "169149177823245", "954301797559301", "5399467787889483", "30631118027908197" ]
[ "nonn" ]
11
0
2
[ "A357232", "A363140" ]
null
Paul D. Hanna, May 17 2023
2023-05-17T12:48:22
oeisdata/seq/A363/A363140.seq
8c9479891e17c01c31a2c4b9831c9925
A363141
Expansion of g.f. A(x) satisfying 1/x = Sum_{n=-oo..+oo} x^n * (A(x) - x^n)^(n-1), with a(0) = 1, a(1) = 1.
[ "1", "1", "0", "2", "3", "11", "23", "76", "188", "575", "1587", "4732", "13714", "40993", "121787", "367100", "1107371", "3367412", "10267404", "31468401", "96734992", "298488537", "923587457", "2866241029", "8916951360", "27808418089", "86910042122", "272180834822", "854004007736", "2684311988984", "8451232727631" ]
[ "nonn" ]
9
0
4
[ "A357227", "A363141", "A363312", "A363313", "A363314", "A363315" ]
null
Paul D. Hanna, Jun 09 2023
2023-06-09T08:57:59
oeisdata/seq/A363/A363141.seq
2df3fc8073137168829c4888e21c6f9b
A363142
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x) + x^(2*n-1))^(n+1).
[ "1", "1", "3", "7", "17", "42", "107", "275", "715", "1884", "5009", "13421", "36224", "98382", "268657", "737244", "2032035", "5622938", "15615186", "43505382", "121570407", "340639265", "956861955", "2694064938", "7601455079", "21490621769", "60870280259", "172707869088", "490818655346", "1396973741672", "3981748142925" ]
[ "nonn" ]
19
0
3
[ "A359670", "A359711", "A363142", "A363143", "A363144", "A363182" ]
null
Paul D. Hanna, May 17 2023
2023-05-23T07:12:55
oeisdata/seq/A363/A363142.seq
936006d3d20665e213f91942c1b04cec
A363143
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x) + x^(3*n-1))^(n+1).
[ "1", "1", "1", "3", "7", "13", "25", "52", "111", "235", "495", "1054", "2271", "4923", "10703", "23354", "51190", "112668", "248783", "550875", "1223107", "2722766", "6075619", "13586390", "30442616", "68339788", "153683822", "346173172", "780948750", "1764312745", "3991321375", "9040912764", "20503640896", "46552634034" ]
[ "nonn" ]
13
0
4
[ "A359711", "A363142", "A363143", "A363144" ]
null
Paul D. Hanna, May 17 2023
2023-05-18T19:22:06
oeisdata/seq/A363/A363143.seq
f1985209f784c45a01184536c9ddadf7
A363144
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x) + x^(4*n-1))^(n+1).
[ "1", "1", "1", "1", "3", "7", "13", "21", "35", "64", "125", "243", "459", "852", "1593", "3035", "5857", "11326", "21835", "42053", "81246", "157741", "307421", "600207", "1172805", "2294197", "4495735", "8827574", "17363422", "34198201", "67429181", "133097669", "263028031", "520406201", "1030749582", "2043553947", "4055171751" ]
[ "nonn" ]
13
0
5
[ "A359711", "A363142", "A363143", "A363144" ]
null
Paul D. Hanna, May 17 2023
2023-05-18T19:23:18
oeisdata/seq/A363/A363144.seq
302794441977e2081079985cb122e9e3
A363145
Number of subsets S of {A007931(1), A007931(2), ..., A007931(n)} with the property that no element of S is a substring of any other.
[ "1", "2", "4", "6", "8", "12", "21", "30", "38", "48", "63", "91", "145", "222", "390", "558", "712", "892", "1142", "1456", "1936", "2464", "3270", "4792", "7690", "11854", "18757", "28733", "47355", "73632", "130315", "186998", "239552", "300347", "388902", "492078", "643230", "816210", "1057438", "1354293", "1804608", "2338124", "3111812" ]
[ "nonn", "base" ]
17
0
2
[ "A007931", "A363145" ]
null
Peter Kagey, May 19 2023
2023-07-15T06:35:23
oeisdata/seq/A363/A363145.seq
588e33634e321483486af7348ef8d475
A363146
Triangle T(n,k) in which the n-th row encodes the inverse of a 3n X 3n Jacobi matrix, with 1's on the lower, main, and upper diagonals in GF(2), where the encoding consists of the decimal representations for the binary rows (n >= 1, 1 <= k <= 3n).
[ "3", "7", "6", "27", "59", "48", "3", "55", "54", "219", "475", "384", "27", "443", "432", "3", "439", "438", "1755", "3803", "3072", "219", "3547", "3456", "27", "3515", "3504", "3", "3511", "3510", "14043", "30427", "24576", "1755", "28379", "27648", "219", "28123", "28032", "27", "28091", "28080", "3", "28087", "28086", "112347", "243419", "196608", "14043", "227035", "221184", "1755", "224987", "224256", "219", "224731" ]
[ "nonn", "tabf" ]
36
1
1
[ "A010701", "A038184", "A083068", "A083233", "A083713", "A125837", "A363146" ]
null
Nei Y. Soma, May 19 2023
2023-05-21T19:28:55
oeisdata/seq/A363/A363146.seq
cbfc6e4e3c8dc76bb91fc91c645fec45
A363147
Primes q == 1 (mod 4) such that there is at least one equivalence class of quaternary quadratic forms of discriminant q not representing 2.
[ "193", "233", "241", "257", "277", "281", "313", "337", "349", "353", "373", "389", "397", "401", "409", "421", "433", "449", "457", "461", "509", "521", "541", "557", "569", "577", "593", "601", "613", "617", "641", "653", "661", "673", "677", "701", "709", "733", "757", "761", "769", "773", "797", "809", "821", "829", "853", "857", "877", "881", "929", "937" ]
[ "nonn" ]
14
1
1
[ "A307250", "A363147", "A363148" ]
null
Andy Huchala, May 18 2023
2023-05-20T01:04:35
oeisdata/seq/A363/A363147.seq
8b7a4e7f0e1122c71574aad26495b949
A363148
a(n) gives the number of equivalence classes of quaternary quadratic forms of discriminant A363147(n) not representing 2.
[ "1", "1", "2", "1", "1", "2", "3", "4", "1", "2", "2", "1", "1", "4", "6", "2", "6", "5", "7", "1", "1", "7", "4", "2", "9", "10", "7", "13", "5", "8", "11", "3", "5", "15", "3", "5", "7", "6", "8", "14", "20", "3", "4", "17", "6", "9", "8", "15", "10", "19", "20", "26", "7", "20", "20", "12", "34", "7", "13", "32", "26", "10", "16", "16", "23", "11", "17", "41", "37", "11", "28", "46", "20", "28", "14", "17" ]
[ "nonn" ]
25
1
3
[ "A307250", "A363147", "A363148" ]
null
Andy Huchala, May 17 2023
2023-05-19T11:07:15
oeisdata/seq/A363/A363148.seq
c42f27333baae89dc55c5b6d1a2be8a3
A363149
Expansion of 1 / Sum_{k>=0} x^(k*(5*k - 3)/2).
[ "1", "-1", "1", "-1", "1", "-1", "1", "-2", "3", "-4", "5", "-6", "7", "-8", "10", "-13", "17", "-22", "27", "-33", "40", "-49", "61", "-77", "98", "-123", "153", "-189", "233", "-288", "358", "-448", "561", "-701", "872", "-1082", "1342", "-1666", "2073", "-2584", "3223", "-4016", "4997", "-6212", "7720", "-9598", "11942", "-14869", "18517", "-23053", "28687" ]
[ "sign" ]
13
0
8
[ "A000566", "A106507", "A308806", "A317665", "A322799", "A361979", "A363149", "A363275" ]
null
Ilya Gutkovskiy, May 25 2023
2023-05-26T08:50:29
oeisdata/seq/A363/A363149.seq
befcc94c74649930d721766b43eece07
A363150
a(n) = numerator(Sum_{j=0..n} Bernoulli(j, 1) * Bernoulli(n - j, 1)).
[ "1", "1", "7", "1", "-7", "-1", "23", "1", "-121", "-1", "481", "5", "-3015581", "-691", "67337", "7", "-30135767", "-3617", "10946836702", "43867", "-369658793327", "-174611", "1633542173485", "854513", "-20836336617617359", "-236364091", "28614002185051", "8553103", "-10503257306519121539", "-23749461029" ]
[ "sign", "frac" ]
18
0
3
[ "A027642", "A164555", "A363150", "A363151", "A363152", "A363153" ]
null
Peter Luschny, May 18 2023
2023-05-19T13:06:39
oeisdata/seq/A363/A363150.seq
a422ad4b75afca1191787238050a5011
A363151
a(n) = denominator(Sum_{j=0..n} Bernoulli(j, 1) * Bernoulli(n - j, 1)).
[ "1", "1", "12", "6", "180", "30", "630", "42", "2100", "30", "3465", "66", "6306300", "2730", "30030", "6", "2187900", "510", "101846745", "798", "355655300", "330", "133855722", "138", "121808707020", "2730", "10140585", "6", "194090796900", "870", "46329473220030", "14322", "4870754760300", "510", "300840735195", "6", "384913687052594700" ]
[ "nonn", "frac" ]
17
0
3
[ "A027642", "A164555", "A363150", "A363151", "A363152", "A363153" ]
null
Peter Luschny, May 18 2023
2023-05-19T13:06:26
oeisdata/seq/A363/A363151.seq
b5262ad205242960a6aa38029565272f
A363152
a(n) = denominator(Sum_{j=0..2*n} Bernoulli(j, 1) * Bernoulli(2*n - j, 1)).
[ "1", "12", "180", "630", "2100", "3465", "6306300", "30030", "2187900", "101846745", "355655300", "133855722", "121808707020", "10140585", "194090796900", "46329473220030", "4870754760300", "300840735195", "384913687052594700", "2473579378270", "100402586963979300", "27473798796507063", "17194486321623468" ]
[ "nonn", "frac" ]
10
0
2
[ "A027642", "A164555", "A363150", "A363151", "A363152", "A363153" ]
null
Peter Luschny, May 18 2023
2023-05-19T05:32:09
oeisdata/seq/A363/A363152.seq
4a6e3d4d15e53a8ff50a6417f1603404
A363153
a(n) = numerator(Sum_{j=0..2*n} Bernoulli(j, 1) * Bernoulli(2*n - j, 1)).
[ "1", "7", "-7", "23", "-121", "481", "-3015581", "67337", "-30135767", "10946836702", "-369658793327", "1633542173485", "-20836336617617359", "28614002185051", "-10503257306519121539", "55315660282703717655037", "-146269786633489194137851", "256962811799649370068488", "-10500086267327643941391664345141" ]
[ "sign", "frac" ]
9
0
2
[ "A027642", "A164555", "A363150", "A363151", "A363152", "A363153" ]
null
Peter Luschny, May 18 2023
2023-05-19T04:37:16
oeisdata/seq/A363/A363153.seq
8fbb5b61bee670b85786e0ac48a03608
A363154
Triangle read by rows. The Hadamard product of A173018 and A349203.
[ "1", "1", "0", "2", "1", "0", "3", "4", "1", "0", "12", "33", "22", "3", "0", "10", "52", "66", "26", "2", "0", "60", "570", "1208", "906", "228", "10", "0", "105", "1800", "5955", "7248", "3573", "600", "15", "0", "280", "8645", "42930", "78095", "62476", "21465", "2470", "35", "0", "252", "14056", "102256", "264702", "312380", "176468", "43824", "3514", "28", "0" ]
[ "nonn", "tabl" ]
10
0
4
[ "A002944", "A099946", "A173018", "A349203", "A362990", "A362994", "A363154" ]
null
Peter Luschny, May 21 2023
2024-05-02T09:45:36
oeisdata/seq/A363/A363154.seq
7d93f54f617ec175937b3795a4f32349
A363155
Expansion of Sum_{k>0} k * x^(3*k-1) / (1 - x^(5*k-2)).
[ "0", "1", "0", "0", "3", "0", "0", "4", "0", "0", "5", "0", "2", "6", "0", "0", "7", "0", "0", "8", "5", "0", "9", "0", "0", "10", "0", "0", "17", "0", "0", "12", "0", "3", "13", "0", "7", "14", "0", "0", "15", "0", "0", "16", "8", "0", "24", "0", "0", "18", "0", "0", "28", "0", "0", "20", "0", "0", "21", "8", "10", "22", "0", "0", "27", "0", "0", "24", "11", "0", "25", "0", "9", "26", "0", "0", "39", "0", "0", "28", "0", "0", "38", "0", "13", "40", "0", "0", "31", "0", "0" ]
[ "nonn" ]
19
1
5
[ "A359288", "A363028", "A363033", "A363155", "A364096", "A364104" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-07T06:38:14
oeisdata/seq/A363/A363155.seq
09ad5bdd836e34b8d15f16b2762df370
A363156
Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-2)).
[ "1", "2", "3", "5", "5", "6", "8", "8", "9", "13", "11", "12", "14", "14", "15", "20", "17", "20", "20", "20", "21", "27", "23", "24", "26", "28", "27", "34", "32", "30", "32", "32", "33", "43", "35", "36", "38", "38", "39", "52", "41", "47", "44", "44", "45", "55", "47", "48", "50", "52", "56", "62", "53", "54", "59", "56", "57", "75", "59", "60", "62", "68", "63", "76", "65", "68", "68", "71", "69", "83", "71", "72", "81", "81", "75", "94", "77", "78", "80" ]
[ "nonn" ]
13
1
2
[ "A359236", "A363034", "A363156" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:28:58
oeisdata/seq/A363/A363156.seq
ccb0c940a84117d20bd58c7dca081e17
A363157
Expansion of Sum_{k>0} k * x^(4*k-1) / (1 - x^(5*k-2)).
[ "0", "0", "1", "0", "0", "1", "2", "0", "1", "0", "3", "1", "0", "0", "7", "0", "0", "1", "5", "0", "1", "0", "8", "4", "0", "0", "8", "0", "0", "1", "10", "0", "5", "0", "9", "1", "3", "0", "13", "0", "0", "6", "11", "0", "1", "0", "14", "1", "0", "3", "24", "0", "0", "1", "16", "0", "1", "0", "15", "8", "0", "0", "22", "0", "5", "1", "17", "0", "13", "0", "20", "1", "0", "0", "20", "3", "0", "10", "28", "0", "1", "0", "21", "1", "0", "0", "39", "5", "3", "1", "23", "0", "8", "0", "26", "12", "0", "0", "26" ]
[ "nonn" ]
13
1
7
[ "A359270", "A363035", "A363157" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:30:54
oeisdata/seq/A363/A363157.seq
b27a992f5130144b910f9ceb9df61049
A363158
Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(5*k-2)).
[ "0", "1", "0", "2", "1", "3", "0", "5", "0", "5", "1", "8", "0", "8", "0", "8", "1", "9", "3", "13", "0", "11", "1", "12", "0", "18", "0", "16", "1", "15", "0", "20", "5", "17", "1", "20", "0", "20", "0", "26", "1", "21", "0", "29", "3", "23", "8", "24", "0", "26", "0", "28", "1", "35", "0", "34", "0", "32", "1", "32", "9", "36", "0", "32", "1", "33", "0", "53", "0", "35", "4", "36", "0", "38", "11", "40", "1", "39", "5", "52", "0", "53", "1", "47", "0", "44", "0" ]
[ "nonn" ]
13
1
4
[ "A359244", "A363053", "A363158" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:31:02
oeisdata/seq/A363/A363158.seq
037613146bd05506c2b233a10fbdcc6a
A363159
a(1)=1. Thereafter, if a(n-1) is a novel term, a(n) is the smallest prime which does not divide a(n-1). If a(n-1) has been seen k (>1) times already then a(n) = k*a(n-1).
[ "1", "2", "3", "2", "4", "3", "6", "5", "2", "6", "12", "5", "10", "3", "9", "2", "8", "3", "12", "24", "5", "15", "2", "10", "20", "3", "15", "30", "7", "2", "12", "36", "5", "20", "40", "3", "18", "5", "25", "2", "14", "3", "21", "2", "16", "3", "24", "48", "5", "30", "60", "7", "14", "28", "3", "27", "2", "18", "36", "72", "5", "35", "2", "20", "60", "120", "7", "21", "42", "5", "40", "80", "3", "30", "90", "7", "28", "56", "3", "33", "2", "22", "3", "36", "108" ]
[ "nonn" ]
47
1
2
[ "A001221", "A002110", "A007947", "A053669", "A321516", "A351495", "A359804", "A363159" ]
null
David James Sycamore, Jul 08 2023
2023-07-15T08:48:18
oeisdata/seq/A363/A363159.seq
f576efdbeb8b9030f1c6d3ab47e0422d
A363160
Smallest positive integer m with all digits distinct such that m^n contains each digit of m exactly n times, or -1 if no such m exists.
[ "1", "406512", "516473892", "5702631489", "961527834", "7025869314", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1" ]
[ "sign", "base" ]
106
1
2
[ "A114258", "A114259", "A114260", "A114261", "A199630", "A199631", "A199632", "A199633", "A363160", "A365144" ]
null
Jean-Marc Rebert, Sep 07 2023
2023-09-10T09:09:35
oeisdata/seq/A363/A363160.seq
94494c570b89911869d310799bab67cb
A363161
Partial sums of A363031.
[ "1", "9", "23", "43", "74", "106", "144", "188", "245", "317", "379", "447", "521", "601", "709", "821", "919", "1023", "1133", "1277", "1410", "1538", "1698", "1838", "2018", "2170", "2328", "2492", "2675", "2923", "3105", "3321", "3515", "3715", "3967", "4179", "4435", "4659", "4889", "5177", "5419", "5699", "5987", "6291", "6615", "6887", "7165", "7449", "7756", "8116", "8468", "8776", "9090", "9450", "9884" ]
[ "nonn", "easy" ]
39
0
2
[ "A016921", "A239660", "A363031", "A363161", "A365442", "A365444", "A365446" ]
null
Omar E. Pol, May 18 2023
2023-10-08T09:32:12
oeisdata/seq/A363/A363161.seq
537cc7e1270c5c9a3968ed0b439193b7
A363162
a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of distinct prime divisors as a(n-2) + a(n-1).
[ "1", "2", "3", "4", "5", "7", "6", "8", "10", "12", "14", "15", "9", "18", "11", "13", "20", "21", "16", "17", "22", "24", "26", "28", "33", "19", "34", "23", "35", "36", "25", "27", "38", "39", "40", "29", "44", "31", "45", "46", "48", "50", "51", "32", "37", "52", "41", "54", "55", "43", "56", "57", "47", "58", "30", "62", "63", "49", "65", "42", "53", "68", "59", "61", "60", "64", "69", "72", "74", "75", "67", "76", "77", "80", "71", "73", "82" ]
[ "nonn" ]
20
1
2
[ "A001221", "A352867", "A355647", "A355649", "A355702", "A363162" ]
null
Scott R. Shannon, Jul 06 2023
2023-07-08T10:42:02
oeisdata/seq/A363/A363162.seq
7ac541f7e2cbd6968da7ffbaa8dc422f
A363163
Number of directed multigraphs without loops containing n edges and an infinite number of vertices modulo isomorphism and reversal of all edge directions.
[ "1", "1", "5", "17", "83", "394", "2278", "13949", "93898", "670003", "5059914", "40033149", "330555726", "2836763749", "25233047351", "232080785282", "2202802051834", "21539083861802", "216638327167235", "2238260395921444", "23725940481578999" ]
[ "nonn" ]
17
0
3
[ "A363163", "A364088" ]
null
Saibal Mitra, Jul 07 2023
2023-08-05T22:32:43
oeisdata/seq/A363/A363163.seq
04f38a34b2709843974bcb0620251ab4
A363164
Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) is the greatest nonnegative number whose binary digits appear in order but not necessarily as consecutive digits in the binary expansions of n and k.
[ "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "2", "1", "0", "0", "1", "1", "1", "1", "0", "0", "1", "2", "3", "2", "1", "0", "0", "1", "2", "1", "1", "2", "1", "0", "0", "1", "2", "3", "4", "3", "2", "1", "0", "0", "1", "1", "3", "2", "2", "3", "1", "1", "0", "0", "1", "2", "3", "2", "5", "2", "3", "2", "1", "0", "0", "1", "2", "1", "1", "3", "3", "1", "1", "2", "1", "0", "0", "1", "2", "3", "4", "3", "6", "3", "4", "3", "2", "1", "0" ]
[ "nonn", "base", "tabl" ]
23
0
13
[ "A175466", "A301983", "A363164" ]
null
Rémy Sigrist, Jul 07 2023
2023-07-13T08:37:57
oeisdata/seq/A363/A363164.seq
8f424ce1abcee4cb050b9c4e5c06962d
A363165
The number of spanning trees of the ladder graph L_n up to automorphisms of L_n.
[ "1", "1", "6", "17", "59", "204", "750", "2746", "10215", "37936", "141468", "527283", "1967449", "7340090", "27392124", "102219380", "381482477", "1423676862", "5313214098", "19829053909", "74002960983", "276182321224", "1030726172586", "3846720619566", "14356155740947", "53577895814828", "199955425410792" ]
[ "nonn", "easy" ]
48
1
3
[ "A001353", "A001835", "A048788", "A363165" ]
null
Mithra Karamchedu and Lucas Bang, Jul 06 2023
2023-07-11T11:17:55
oeisdata/seq/A363/A363165.seq
08b4beaf138c1e842c17cf8a2a00a61b
A363166
Bouton numbers: a(n) is the number of P positions in games of Nim with three nonzero heaps each containing at most n sticks.
[ "0", "0", "1", "1", "2", "4", "7", "7", "8", "10", "13", "17", "22", "28", "35", "35", "36", "38", "41", "45", "50", "56", "63", "71", "80", "90", "101", "113", "126", "140", "155", "155", "156", "158", "161", "165", "170", "176", "183", "191", "200", "210", "221", "233", "246", "260", "275", "291", "308", "326", "345", "365", "386", "408", "431", "455", "480", "506", "533", "561", "590", "620", "651", "651", "652" ]
[ "easy", "nonn" ]
17
1
5
null
null
Peter Rowlett, Jul 06 2023
2023-08-05T22:45:54
oeisdata/seq/A363/A363166.seq
0d6524e62bb7136765d77f675803fa6e
A363167
Products of four distinct strong primes.
[ "200651", "222343", "283679", "319957", "363341", "385033", "408221", "428417", "452353", "463573", "483923", "491249", "513689", "526031", "544357", "546601", "547723", "580261", "605693", "671143", "688721", "696377", "698819", "739211", "740333", "742951", "743699", "747881", "771661", "774367", "783343", "790801", "808027", "820369" ]
[ "nonn" ]
58
1
1
[ "A046386", "A051634", "A363167", "A363782", "A364778" ]
null
Massimo Kofler, Sep 07 2023
2023-10-08T09:44:11
oeisdata/seq/A363/A363167.seq
64fe3244115f70dd77976f1dc4a5e5f1
A363168
Balanced primes of order 100.
[ "27947", "111337", "193283", "197341", "197621", "347063", "809821", "955193", "1029803", "1184269", "1292971", "1609163", "1630859", "1656019", "1752449", "1883381", "1935517", "1969661", "2120221", "2156383", "2238959", "2287133", "2548631", "2592089", "2750903", "2866403", "3165769", "3257941", "3590299", "3889423" ]
[ "nonn" ]
25
1
1
[ "A006562", "A082077", "A082078", "A082079", "A096697", "A096698", "A096699", "A096700", "A096701", "A096702", "A096703", "A096704", "A300364", "A300365", "A363168" ]
null
Harvey P. Dale, Jul 07 2023
2023-07-23T01:53:38
oeisdata/seq/A363/A363168.seq
04168486214d02f0065c3cf3a24dc769
A363169
Powerful abundant numbers: numbers that are both powerful (A001694) and abundant (A005101).
[ "36", "72", "100", "108", "144", "196", "200", "216", "288", "324", "392", "400", "432", "500", "576", "648", "784", "800", "864", "900", "968", "972", "1000", "1152", "1296", "1352", "1372", "1568", "1600", "1728", "1764", "1800", "1936", "1944", "2000", "2304", "2500", "2592", "2700", "2704", "2744", "2916", "3136", "3200", "3456", "3528", "3600", "3872", "3888", "4000" ]
[ "nonn" ]
13
1
1
[ "A001694", "A005101", "A180114", "A307959", "A328136", "A356871", "A363169", "A363170", "A363171" ]
null
Amiram Eldar, May 19 2023
2025-04-22T21:55:38
oeisdata/seq/A363/A363169.seq
cf78b5d4c191c955ab764cdc82a061da
A363170
The number of powerful abundant numbers (A363169) not exceeding 10^n.
[ "0", "3", "23", "82", "297", "1000", "3268", "10534", "33799", "107901", "343155", "1090189", "3460380", "10970774", "34749182", "109991778", "348006756", "1101058505", "3483105232", "11017518803" ]
[ "nonn", "more" ]
5
1
2
[ "A001694", "A005101", "A118896", "A302992", "A363169", "A363170" ]
null
Amiram Eldar, May 19 2023
2023-05-19T06:14:54
oeisdata/seq/A363/A363170.seq
7344b1de5e22117a07730343ac0b617e
A363171
Numbers k such that A064549(k) is an abundant number (A005101).
[ "6", "10", "12", "14", "18", "20", "24", "28", "30", "36", "40", "42", "44", "48", "50", "52", "54", "56", "60", "66", "70", "72", "78", "80", "84", "88", "90", "96", "98", "100", "102", "104", "105", "108", "110", "112", "114", "120", "126", "130", "132", "136", "138", "140", "144", "150", "152", "154", "156", "160", "162", "168", "170", "174", "176", "180", "182", "184", "186" ]
[ "nonn" ]
8
1
1
[ "A003557", "A005101", "A064549", "A334166", "A363169", "A363171", "A363172" ]
null
Amiram Eldar, May 19 2023
2023-05-19T06:14:11
oeisdata/seq/A363/A363171.seq
0eb842a4cdc8a7d60e589e3001241583
A363172
Primitive terms of A363171: terms of A363171 with no proper divisor in A363171.
[ "6", "10", "14", "44", "52", "105", "136", "152", "184", "232", "248", "286", "374", "418", "442", "495", "506", "592", "656", "688", "752", "848", "944", "976", "1292", "1564", "1748", "1755", "1972", "2108", "2144", "2145", "2204", "2272", "2336", "2356", "2516", "2528", "2656", "2668", "2788", "2805", "2812", "2848", "2852", "2924", "2925", "3104", "3116" ]
[ "nonn" ]
7
1
1
[ "A363171", "A363172" ]
null
Amiram Eldar, May 19 2023
2023-05-19T06:15:21
oeisdata/seq/A363/A363172.seq
b951f037858846853c68b14fead4767c
A363173
Number of triangles inside a regular n-gon formed by intersecting line segments, considering all configurations of 3 line segments from 6 distinct vertices.
[ "0", "0", "0", "0", "7", "16", "84", "180", "462", "796", "1716", "2856", "5005", "7744", "12376", "17508", "27132", "38160", "54264", "73788", "100947", "132216", "177100", "228748", "296010", "374808", "475020", "584140", "736281", "903168", "1107568", "1341232", "1623160", "1939308", "2324784", "2755380", "3262623", "3832080", "4496388" ]
[ "nonn" ]
29
3
5
[ "A000579", "A006561", "A260417", "A363173", "A363174" ]
null
Paolo Xausa, May 19 2023
2023-06-27T10:28:09
oeisdata/seq/A363/A363173.seq
343d724971f0dc7face17bee967957d6
A363174
Array read by rows: T(n,k) is the number of triangles inside a regular n-gon formed by intersecting line segments, considering all configurations of 3 line segments from k distinct vertices, with n >= 3, 3 <= k <= 6.
[ "1", "0", "0", "0", "4", "4", "0", "0", "10", "20", "5", "0", "20", "60", "30", "0", "35", "140", "105", "7", "56", "280", "280", "16", "84", "504", "630", "84", "120", "840", "1260", "180", "165", "1320", "2310", "462", "220", "1980", "3960", "796", "286", "2860", "6435", "1716", "364", "4004", "10010", "2856", "455", "5460", "15015", "5005", "560", "7280", "21840", "7744" ]
[ "nonn", "tabf" ]
37
3
5
[ "A000292", "A000579", "A006561", "A006600", "A033488", "A174002", "A260417", "A363173", "A363174" ]
null
Paolo Xausa, May 19 2023
2024-11-26T08:42:04
oeisdata/seq/A363/A363174.seq
63852f51197436daa3652b6ec10ee38e
A363175
Primitive abundant numbers (A071395) that are powerful numbers (A001694).
[ "342225", "570375", "3172468", "4636684", "63126063", "99198099", "117234117", "171991125", "280495504", "319600125", "327921075", "404529741", "581549787", "635689593", "762155163", "1029447225", "1148667664", "1356949503", "1435045924", "1501500375", "1558495125", "1596961444", "1757705625", "1778362047" ]
[ "nonn" ]
13
1
1
[ "A001694", "A036966", "A071395", "A306796", "A306797", "A363169", "A363175", "A363176", "A363177" ]
null
Amiram Eldar, May 19 2023
2023-05-19T08:02:19
oeisdata/seq/A363/A363175.seq
e0385b4c2c92aee332994749b5966d23
A363176
Primitive abundant numbers (A091191) that are powerful numbers (A001694).
[ "196", "15376", "342225", "570375", "1032256", "3172468", "4636684", "63126063", "99198099", "117234117", "171991125", "280495504", "319600125", "327921075", "404529741", "581549787", "635689593", "762155163", "1029447225", "1148667664", "1356949503", "1435045924", "1501500375", "1558495125", "1596961444", "1757705625" ]
[ "nonn" ]
10
1
1
[ "A001694", "A036966", "A091191", "A363169", "A363175", "A363176" ]
null
Amiram Eldar, May 19 2023
2023-05-19T08:02:16
oeisdata/seq/A363/A363176.seq
c3c3713292bd208c0c4f6325c5e0c9db
A363177
Primitive abundant numbers (A071395) that are cubefull numbers (A036966).
[ "26376098024367", "33912126031329", "1910383099764867", "2792098376579421", "5229860083034911875", "6886512413632368153", "8815747507513708671", "28966027524687899919", "42200802302982406288", "89594138836162749375", "224439112362213402759", "288564573037131517833", "512767531125033485625" ]
[ "nonn" ]
10
1
1
[ "A036966", "A036967", "A071395", "A091191", "A306797", "A363169", "A363175", "A363177" ]
null
Amiram Eldar, May 19 2023
2023-05-19T08:02:24
oeisdata/seq/A363/A363177.seq
a7eae07ffe25eb4223555aa972caa566
A363178
Decimal expansion of Product_{k>=1} (1 - exp(-13*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "8", "1", "6", "7", "2", "3", "2", "3", "9", "4", "3", "2", "8", "4", "2", "2", "4", "2", "8", "1", "7", "7", "0", "0", "1", "1", "3", "8", "5", "4", "7", "3", "8", "9", "8", "9", "0", "7", "3", "2", "2", "1", "9", "5", "5", "3", "9", "6", "6", "6", "7", "7", "7", "1", "1", "6", "0", "8", "7", "8", "9", "3", "0", "1", "3", "7", "1", "5", "1", "9", "2", "9", "8", "4", "6", "8", "4", "9", "8", "8", "2", "6", "3", "1", "6", "0", "9", "2", "4" ]
[ "nonn", "cons" ]
5
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 19 2023
2023-05-19T14:21:54
oeisdata/seq/A363/A363178.seq
31d502a4c45aef44caeee7d64ba5382b
A363179
Decimal expansion of Product_{k>=1} (1 - exp(-15*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "6", "5", "7", "7", "4", "1", "1", "4", "5", "5", "8", "7", "8", "7", "5", "9", "1", "3", "2", "1", "9", "2", "0", "8", "5", "4", "4", "7", "3", "4", "8", "9", "1", "0", "6", "1", "9", "1", "4", "0", "0", "1", "3", "9", "9", "8", "5", "6", "2", "8", "4", "4", "1", "8", "9", "2", "9", "8", "6", "8", "0", "6", "4", "2", "7", "6", "6", "1", "1", "7", "3", "6", "6", "7", "5", "6", "5", "5", "0", "1", "5", "3", "8", "1", "7", "8" ]
[ "nonn", "cons" ]
4
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 19 2023
2023-05-19T14:22:00
oeisdata/seq/A363/A363179.seq
80ffd09f5f1fbf5f149e111ab95b01d0
A363180
Number of permutations of [2n] with n parity changes.
[ "1", "2", "8", "288", "10368", "1036800", "103680000", "20321280000", "3982970880000", "1290482565120000", "418116351098880000", "202368313931857920000", "97946263943019233280000", "66211674425481001697280000", "44759091911625157147361280000", "40283182720462641432625152000000" ]
[ "nonn" ]
38
0
2
[ "A152874", "A363180", "A363236" ]
null
Alois P. Heinz, May 23 2023
2023-05-26T08:18:50
oeisdata/seq/A363/A363180.seq
a92fad84b265a17445b7ca71e2177c8f
A363181
Number of permutations p of [n] such that for each i in [n] we have: (i>1) and |p(i)-p(i-1)| = 1 or (i<n) and |p(i)-p(i+1)| = 1.
[ "1", "0", "2", "2", "8", "14", "54", "128", "498", "1426", "5736", "18814", "78886", "287296", "1258018", "4986402", "22789000", "96966318", "461790998", "2088374592", "10343408786", "49343711666", "253644381032", "1268995609502", "6756470362374", "35285321738624", "194220286045506", "1054759508543554" ]
[ "nonn" ]
43
0
3
[ "A002464", "A003274", "A011655", "A095816", "A127697", "A179957", "A211694", "A229730", "A271212", "A333833", "A346462", "A363181", "A363236" ]
null
Alois P. Heinz, May 19 2023
2025-02-07T12:02:10
oeisdata/seq/A363/A363181.seq
35924a03f6afdcd9bb44c5340c416732
A363182
Expansion of g.f. A(x) satisfying 2 = Sum_{n=-oo..+oo} (-1)^n * x^n * (2*A(x) + x^(2*n-1))^(n+1).
[ "1", "2", "6", "20", "68", "234", "824", "2956", "10750", "39540", "146864", "550096", "2075432", "7880046", "30086704", "115445028", "444941028", "1721720032", "6686357238", "26051961396", "101810056296", "398962013908", "1567354966200", "6171824148252", "24355381522328", "96304034538898", "381506619687824" ]
[ "nonn" ]
8
0
2
[ "A359670", "A363142", "A363182", "A363183", "A363184", "A363185" ]
null
Paul D. Hanna, May 20 2023
2023-05-21T00:44:04
oeisdata/seq/A363/A363182.seq
bb4fd047de9509a8fac6656afb3d6773
A363183
Expansion of g.f. A(x) satisfying 3 = Sum_{n=-oo..+oo} (-1)^n * x^n * (3*A(x) + x^(2*n-1))^(n+1).
[ "1", "3", "11", "45", "193", "846", "3779", "17169", "79115", "368820", "1736169", "8241039", "39400672", "189567594", "917146729", "4459208292", "21776797603", "106771412718", "525382657858", "2593665077634", "12842387591191", "63762186132387", "317373771999035", "1583380006374078", "7916456438276103" ]
[ "nonn" ]
7
0
2
[ "A359670", "A363142", "A363182", "A363183", "A363184", "A363185" ]
null
Paul D. Hanna, May 20 2023
2023-05-21T00:44:08
oeisdata/seq/A363/A363183.seq
bf0f6d64a44d54951f3f584a012e00b1
A363184
Expansion of g.f. A(x) satisfying 4 = Sum_{n=-oo..+oo} (-1)^n * x^n * (4*A(x) + x^(2*n-1))^(n+1).
[ "1", "4", "18", "88", "452", "2388", "12872", "70520", "391630", "2199816", "12476024", "71341184", "410864744", "2381026908", "13874518912", "81244555896", "477825991140", "2821333839872", "16718050009866", "99385412418648", "592575029005992", "3542752436877800", "21233468105000280", "127555885796445432" ]
[ "nonn" ]
11
0
2
[ "A359670", "A363142", "A363182", "A363183", "A363184", "A363185" ]
null
Paul D. Hanna, May 20 2023
2023-05-23T14:28:45
oeisdata/seq/A363/A363184.seq
87478ebdb1ef14b9c6f82b1e633b3b3c
A363185
Expansion of g.f. A(x) satisfying 5 = Sum_{n=-oo..+oo} (-1)^n * x^n * (5*A(x) + x^(2*n-1))^(n+1).
[ "1", "5", "27", "155", "929", "5730", "36083", "230935", "1497739", "9822060", "65021849", "433937545", "2916359840", "19720710150", "134078691289", "915994242780", "6284957607075", "43291450899490", "299248617182754", "2075172105905550", "14432704539830007", "100648564848019045", "703624464015723819" ]
[ "nonn" ]
5
0
2
[ "A359670", "A363142", "A363182", "A363183", "A363184", "A363185" ]
null
Paul D. Hanna, May 20 2023
2023-05-21T00:44:19
oeisdata/seq/A363/A363185.seq
8b3f5dce44c08f77be5a824594bac300
A363186
Lexicographically earliest sequence of distinct positive integers such that the sum of all terms a(1)..a(n) is a substring of the concatenation of all terms a(1)..a(n).
[ "1", "10", "98", "767", "111", "122", "2", "11", "100", "889", "110", "4490", "400", "560", "1096", "124", "20", "129", "70", "502", "93", "171", "212", "361", "512", "26", "21", "36", "54", "14", "1011", "139", "99", "59", "550", "684", "345", "102", "1021", "1999", "2871", "137", "892", "89", "126", "875", "510", "994", "586", "2012", "662", "1836", "201", "405", "388", "2007", "2798", "1641", "50", "340" ]
[ "nonn", "base" ]
17
1
2
[ "A300000", "A339144", "A357082", "A359482", "A363186" ]
null
Scott R. Shannon and Eric Angelini, Jul 07 2023
2024-02-08T09:46:24
oeisdata/seq/A363/A363186.seq
052aaef298a2ab7aad7da33181efd95f
A363187
Prime numbers that are the average of three consecutive odd semiprimes.
[ "31", "41", "59", "83", "107", "139", "163", "191", "197", "281", "311", "383", "397", "443", "521", "673", "677", "757", "821", "887", "997", "1061", "1109", "1151", "1171", "1229", "1237", "1373", "1423", "1453", "1619", "1823", "1889", "1931", "2053", "2141", "2203", "2221", "2309", "2339", "2437", "2473", "2477", "2749", "2801", "2837", "2953", "3019", "3119", "3163", "3209", "3257", "3347" ]
[ "nonn" ]
25
1
1
[ "A000040", "A046315", "A363074", "A363187", "A363188" ]
null
Elmo R. Oliveira, May 20 2023
2023-07-11T11:28:00
oeisdata/seq/A363/A363187.seq
fe451aaebcc53a37e407ea29cb2cc60c
A363188
Prime numbers that are the exact average of four consecutive odd semiprimes.
[ "53", "67", "89", "199", "223", "277", "349", "439", "449", "461", "487", "491", "499", "523", "557", "569", "643", "683", "877", "883", "929", "941", "1069", "1153", "1259", "1361", "1471", "1487", "1733", "1787", "1901", "1933", "1951", "2111", "2129", "2251", "2297", "2311", "2371", "2521", "2557", "2689", "2777", "2797", "2861", "2917", "2939", "3037", "3041", "3253", "3259", "3271", "3407" ]
[ "nonn" ]
18
1
1
[ "A000040", "A046315", "A363074", "A363187", "A363188" ]
null
Elmo R. Oliveira, May 20 2023
2023-07-05T12:18:56
oeisdata/seq/A363/A363188.seq
2c1e9480af041ffe4cfc112f5622bcc8
A363189
Indices of the odd terms in the sequence of powerful numbers (A001694).
[ "1", "4", "6", "7", "10", "13", "16", "17", "20", "24", "25", "28", "30", "31", "35", "39", "41", "43", "45", "48", "51", "56", "57", "60", "62", "63", "65", "68", "71", "75", "79", "82", "83", "84", "87", "90", "94", "97", "98", "99", "102", "103", "105", "107", "110", "114", "117", "120", "122", "125", "127", "129", "133", "138", "141", "142", "144", "145", "148", "151", "152" ]
[ "nonn", "easy" ]
9
1
2
[ "A001694", "A062739", "A363189", "A363190", "A363191", "A363192" ]
null
Amiram Eldar, May 21 2023
2023-05-21T12:56:31
oeisdata/seq/A363/A363189.seq
2f9e95ea5151037cb1b9dfecf267ff14
A363190
Odd powerful numbers (A062739) k such that the next powerful number after k is also odd.
[ "25", "121", "225", "343", "1089", "1323", "2187", "2197", "3025", "3087", "3249", "5929", "6125", "6859", "7803", "8575", "9261", "10125", "11881", "11907", "14161", "15125", "16641", "16807", "19683", "19773", "21025", "22707", "25921", "27889", "29241", "29791", "30375", "33275", "36125", "41067", "42849", "44217", "45125", "45369", "49729" ]
[ "nonn", "easy" ]
8
1
1
[ "A001694", "A062739", "A076445", "A363189", "A363190", "A363191", "A363192" ]
null
Amiram Eldar, May 21 2023
2023-05-21T12:56:05
oeisdata/seq/A363/A363190.seq
5fcb2c735886fd4eddde53b843efc79b
A363191
a(n) is the least start of a run of exactly n consecutive powerful numbers (A001694) that are even, or -1 if no such run exists.
[ "16", "4", "196", "968", "8712", "437400", "85730400", "5030690600", "264615012500", "5239012864", "550886816376", "2494017320776852" ]
[ "nonn", "more" ]
7
1
1
[ "A001694", "A062739", "A349062", "A363189", "A363190", "A363191", "A363192" ]
null
Amiram Eldar, May 21 2023
2023-05-21T12:56:09
oeisdata/seq/A363/A363191.seq
d667b52c1706369014fcc2257b92e6fb
A363192
a(n) is the least start of a run of exactly n consecutive powerful numbers (A001694) that are odd, or -1 if no such run exists.
[ "1", "25", "2187", "703125", "93096125", "10229709861", "197584409639", "32044275110699", "164029657560618375" ]
[ "nonn", "more" ]
9
1
2
[ "A001694", "A062739", "A349062", "A363189", "A363190", "A363191", "A363192" ]
null
Amiram Eldar, May 21 2023
2023-05-21T12:56:13
oeisdata/seq/A363/A363192.seq
e525941add7ea1e90ed6ab25d79643ac
A363193
a(1)=1, and thereafter a(n) = number of occurrences of a(k) among terms a(1..k), where k = n-a(n-1).
[ "1", "1", "2", "2", "1", "3", "2", "1", "4", "1", "5", "3", "5", "1", "6", "5", "2", "3", "3", "4", "4", "3", "2", "5", "2", "4", "5", "5", "4", "4", "5", "5", "6", "6", "5", "7", "6", "8", "7", "2", "2", "7", "1", "7", "1", "8", "2", "2", "9", "8", "7", "8", "8", "2", "5", "5", "4", "11", "10", "3", "1", "9", "11", "5", "6", "6", "9", "1", "10", "6", "5", "3", "7", "3", "7", "2", "7", "13", "6", "8", "6", "12", "13", "13", "7", "8" ]
[ "nonn", "easy" ]
31
1
3
[ "A354971", "A363193" ]
null
Neal Gersh Tolunsky, May 20 2023
2023-05-24T19:55:04
oeisdata/seq/A363/A363193.seq
8b724ecc2be87506f0d8183ea0899207
A363194
Number of divisors of the n-th powerful number A001694(n).
[ "1", "3", "4", "3", "5", "3", "4", "6", "9", "3", "7", "12", "5", "9", "12", "3", "4", "8", "15", "3", "9", "12", "16", "9", "6", "9", "18", "3", "15", "4", "3", "12", "15", "20", "9", "9", "12", "10", "3", "21", "5", "20", "12", "9", "7", "15", "18", "3", "24", "27", "3", "12", "18", "16", "11", "9", "12", "24", "9", "9", "25", "12", "4", "12", "3", "12", "9", "9", "18", "21", "3", "28", "27", "36", "3", "15" ]
[ "nonn", "easy" ]
26
1
2
[ "A000005", "A001694", "A072048", "A076400", "A180114", "A306458", "A343443", "A363194", "A363195" ]
null
Amiram Eldar, May 21 2023
2024-09-21T14:47:16
oeisdata/seq/A363/A363194.seq
a3708603438ae6b44a0f9044d79abd2d
A363195
Number of divisors of the n-th cubefull number A036966(n).
[ "1", "4", "5", "4", "6", "7", "5", "4", "8", "16", "6", "9", "4", "20", "10", "5", "20", "7", "24", "16", "11", "25", "4", "28", "24", "20", "12", "8", "4", "5", "30", "16", "6", "16", "32", "30", "24", "13", "4", "20", "35", "20", "28", "9", "4", "36", "36", "28", "14", "16", "25", "20", "40", "16", "24", "35", "4", "40", "5", "42", "7", "32", "15", "6", "20", "32", "16", "20", "10", "30", "45", "20" ]
[ "nonn", "easy" ]
24
1
2
[ "A000005", "A036966", "A072048", "A076400", "A362986", "A363194", "A363195" ]
null
Amiram Eldar, May 21 2023
2024-09-21T14:46:41
oeisdata/seq/A363/A363195.seq
7db161239735b1a0a2ab34af86d09367
A363196
a(n) is the least k such that the rightmost 7 in the decimal expansion of 3^k is in the (10^n)'s position, or -1 if there is no such k.
[ "3", "-1", "6", "37", "50", "14", "18", "38", "28", "25", "48", "188", "34", "93", "45", "40", "44", "134", "54", "60", "96", "86", "61", "81", "229", "57", "133", "321", "89", "412", "628", "210", "200", "257", "429", "256", "313", "672", "885", "530", "2418", "649", "270", "641", "848", "258", "2676", "121", "450", "1448", "3254", "696", "9857", "4961", "804", "6101", "1049", "1476", "5044", "3186", "437", "12560" ]
[ "sign", "base" ]
10
0
1
[ "A000244", "A363196" ]
null
Robert Israel, May 20 2023
2023-05-25T07:51:44
oeisdata/seq/A363/A363196.seq
f7f53c3a9dbfc537321499fc2b2d2e1e
A363197
a(n) is the number of ways the labels 1 to 2^n-1 can be assigned to a perfect binary tree with n levels such that there is an ordering between children and parents and also an ordering between the left and the right child.
[ "1", "1", "10", "343200", "73082837755699200000", "79548797573848497198355214730517854838277265162240000000000" ]
[ "nonn" ]
27
1
3
[ "A056972", "A076615", "A363197" ]
null
Thomas Scheuerle, May 21 2023
2023-07-08T16:46:28
oeisdata/seq/A363/A363197.seq
3e3bb0e64fbab72eae465ef904bc6b19
A363198
a(n) = n for n <= 3; for n >= 4, a(n) is the smallest positive integer that has not appeared previously in this sequence and shares a factor with a(n-1) + a(n-2) + a(n-3).
[ "1", "2", "3", "4", "6", "13", "23", "7", "43", "73", "9", "5", "12", "8", "10", "14", "16", "15", "18", "21", "20", "59", "22", "101", "24", "27", "19", "25", "71", "30", "26", "127", "33", "28", "32", "31", "35", "34", "36", "39", "109", "38", "40", "11", "89", "42", "44", "45", "131", "46", "37", "48", "262", "347", "51", "50", "49", "52", "151", "54", "257", "55", "56", "58", "65" ]
[ "nonn", "easy" ]
41
1
2
[ "A064413", "A337136", "A363198" ]
null
Yifan Xie, May 21 2023
2023-12-30T23:07:49
oeisdata/seq/A363/A363198.seq
d4e3d47d153b2ff940c5316c50662e80
A363199
Number of free tree-like polycubes of size n, identifying rotations but not reflections.
[ "1", "1", "2", "7", "27", "138", "822", "5154", "33880", "227495", "1554266", "10749089", "75106906" ]
[ "nonn", "hard", "more" ]
18
1
3
null
null
Joerg Arndt and Márk Péter Légrádi, May 21 2023
2023-12-11T08:23:24
oeisdata/seq/A363/A363199.seq
6d96716066608e3ac5f421976d463045
A363200
Number of connected animals formed from n 6-gon connected truncated octahedra, avoiding connected squares.
[ "1", "1", "2", "5", "15", "55", "248", "1256", "6844", "38930", "226961", "1345641", "8072770", "48882245", "298237393" ]
[ "nonn", "hard", "more" ]
24
1
3
null
null
Joerg Arndt and Márk Péter Légrádi, May 22 2023
2023-12-09T04:59:23
oeisdata/seq/A363/A363200.seq
b893eff17440bb577497dba2cf5d960a