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int64
-14,827
666,262,453B
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A361701
Constant term in the expansion of (1 + x^4 + y^4 + z^4 + 1/(x*y*z))^n.
[ "1", "1", "1", "1", "1", "1", "1", "211", "1681", "7561", "25201", "69301", "166321", "360361", "990991", "5405401", "34834801", "187867681", "833709241", "3153281041", "10491944401", "31945216801", "97323704941", "345845431471", "1529597398561", "7451402805001", "35092646589001", "151591791651301" ]
[ "nonn", "easy" ]
15
0
8
[ "A361637", "A361658", "A361673", "A361677", "A361701" ]
null
Seiichi Manyama, Mar 21 2023
2023-03-22T07:54:33
oeisdata/seq/A361/A361701.seq
d8384268d061f6731fc4975776b7fbda
A361702
Lexicographically earliest sequence of positive numbers on a square spiral such that no four equal numbers lie on the circumference of a circle.
[ "1", "1", "1", "2", "1", "2", "1", "2", "2", "2", "1", "3", "3", "1", "3", "3", "3", "2", "2", "3", "2", "4", "4", "4", "2", "1", "2", "3", "4", "3", "4", "4", "5", "5", "5", "5", "1", "1", "5", "4", "3", "4", "6", "5", "6", "6", "4", "3", "2", "1", "5", "4", "1", "6", "3", "4", "2", "5", "6", "5", "6", "7", "6", "7", "3", "1", "5", "7", "7", "6", "4", "6", "5", "7", "6", "4", "7", "8", "7", "6", "7", "4", "7", "5", "8", "8", "8", "6", "3", "6", "4", "8", "5", "8", "9", "9", "7", "8", "3" ]
[ "nonn" ]
16
1
4
[ "A174344", "A229037", "A274640", "A274923", "A346294", "A361486", "A361702" ]
null
Scott R. Shannon, Mar 21 2023
2023-04-04T07:46:55
oeisdata/seq/A361/A361702.seq
cfd15486058753973f6177444cc1f8e1
A361703
Constant term in the expansion of (1 + w + x + y + z + 1/(w*x*y*z))^n.
[ "1", "1", "1", "1", "1", "121", "721", "2521", "6721", "15121", "143641", "1302841", "7579441", "32586841", "113753641", "509068561", "3599319361", "25076993761", "142188273361", "662296228561", "2933770097881", "15581813723281", "99333170493481", "623696622059281", "3466773281312881", "17406784944114721" ]
[ "nonn", "easy" ]
17
0
6
[ "A344560", "A361637", "A361675", "A361703", "A361704", "A361705" ]
null
Seiichi Manyama, Mar 21 2023
2023-03-25T07:00:41
oeisdata/seq/A361/A361703.seq
3ac919476c274a9b9b49711771b80ea1
A361704
Constant term in the expansion of (1 + w^2 + x^2 + y^2 + z^2 + 1/(w*x*y*z))^n.
[ "1", "1", "1", "1", "1", "1", "361", "2521", "10081", "30241", "75601", "166321", "1580041", "16833961", "114594481", "569368801", "2273150881", "7723366561", "30024671041", "193227592321", "1460787267601", "9492136169041", "50996729017081", "232560967743721", "973251617544361", "4464217099881001" ]
[ "nonn", "easy" ]
10
0
7
[ "A361675", "A361703", "A361704", "A361705" ]
null
Seiichi Manyama, Mar 21 2023
2023-03-25T07:48:25
oeisdata/seq/A361/A361704.seq
af54087dc84f91869c20e6ef423ff6c3
A361705
Constant term in the expansion of (1 + w^4 + x^4 + y^4 + z^4 + 1/(w*x*y*z))^n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1681", "15121", "75601", "277201", "831601", "2162161", "5045041", "10810801", "54054001", "592191601", "5035670641", "31553973361", "157346607601", "660308770801", "2420415874801", "7951853614321", "24853781309281", "91246800876001", "497098157556001", "3346262924004001" ]
[ "nonn", "easy" ]
11
0
9
[ "A361657", "A361658", "A361675", "A361703", "A361704", "A361705" ]
null
Seiichi Manyama, Mar 21 2023
2023-03-25T07:12:09
oeisdata/seq/A361/A361705.seq
e490e2cdbfc959f170dc4c2b33fe6276
A361706
Inverse Moebius transform applied twice to primes.
[ "2", "7", "9", "19", "15", "37", "21", "50", "39", "65", "35", "116", "45", "91", "87", "134", "63", "174", "71", "200", "125", "155", "87", "322", "125", "197", "172", "282", "113", "383", "131", "349", "217", "271", "213", "555", "161", "311", "267", "546", "183", "555", "195", "482", "402", "379", "215", "857", "267", "546", "369", "602", "245", "768", "349", "774", "421", "503", "281", "1204", "287", "561", "582", "875", "425" ]
[ "nonn" ]
16
1
1
[ "A000005", "A000040", "A007429", "A007445", "A361706", "A361707" ]
null
Ilya Gutkovskiy, Mar 21 2023
2023-03-23T15:56:27
oeisdata/seq/A361/A361706.seq
35bf76070b1f459a397709d3a703de5b
A361707
Moebius transform applied twice to primes.
[ "2", "-1", "1", "3", "7", "5", "13", "8", "15", "9", "27", "10", "37", "11", "23", "22", "55", "8", "63", "18", "37", "19", "79", "12", "77", "21", "62", "32", "105", "-5", "123", "44", "73", "23", "101", "23", "153", "31", "83", "44", "175", "7", "187", "60", "84", "35", "207", "38", "195", "20", "113", "72", "237", "18", "181", "76", "133", "55", "273", "34", "279", "41", "148", "102", "217" ]
[ "sign", "look" ]
16
1
1
[ "A000040", "A007427", "A007431", "A007444", "A361706", "A361707" ]
null
Ilya Gutkovskiy, Mar 21 2023
2023-04-02T12:38:34
oeisdata/seq/A361/A361707.seq
73199cde66b59a1797f5003a25169dfd
A361708
Inverse Moebius transform of nonprimes.
[ "1", "5", "7", "13", "10", "21", "13", "27", "22", "30", "19", "49", "22", "39", "40", "52", "27", "63", "29", "68", "51", "56", "35", "98", "46", "64", "61", "87", "43", "114", "46", "98", "73", "80", "72", "142", "53", "87", "83", "138", "58", "145", "61", "126", "118", "103", "66", "189", "81", "135", "103", "144", "75", "177", "104", "178", "113", "127", "82", "254", "85", "135", "152", "185", "119" ]
[ "nonn", "look" ]
7
1
2
[ "A007445", "A018252", "A361708", "A361709" ]
null
Ilya Gutkovskiy, Mar 21 2023
2023-03-23T19:33:17
oeisdata/seq/A361/A361708.seq
1b7c623297024bf737d112ccbf37953e
A361709
Moebius transform of nonprimes.
[ "1", "3", "5", "4", "8", "1", "11", "6", "9", "4", "17", "6", "20", "7", "10", "11", "25", "8", "27", "10", "15", "12", "33", "9", "27", "14", "24", "14", "41", "12", "44", "21", "25", "20", "30", "14", "51", "23", "29", "20", "56", "15", "59", "25", "30", "27", "64", "20", "56", "26", "39", "30", "73", "24", "50", "31", "45", "35", "80", "18", "83", "37", "45", "41", "59", "26", "90", "39", "54", "30" ]
[ "nonn" ]
4
1
2
[ "A007444", "A018252", "A361708", "A361709" ]
null
Ilya Gutkovskiy, Mar 21 2023
2023-04-09T22:22:51
oeisdata/seq/A361/A361709.seq
1ba383c954afefc06cf77d52afdffdfb
A361710
a(n) = Sum_{k = 0..n-1} (-1)^k*binomial(n,k)*binomial(n-1,k)^2.
[ "0", "1", "-1", "-8", "15", "126", "-280", "-2400", "5775", "50050", "-126126", "-1100736", "2858856", "25069968", "-66512160", "-585307008", "1577585295", "13919870250", "-37978905250", "-335813478000", "925166131890", "8194328596740", "-22754499243840", "-201822515032320", "564121960420200", "5009403008531376" ]
[ "sign", "easy" ]
23
0
4
[ "A005258", "A006480", "A245086", "A361710", "A361711", "A361716" ]
null
Peter Bala, Mar 21 2023
2023-07-27T08:13:02
oeisdata/seq/A361/A361710.seq
febf9c91f47ed8e5a8eda2f78b11f30d
A361711
a(1) = 1 and a(n) = Sum_{k = 0..n-2} (-1)^k * binomial(n,k)^2 * binomial(n-2,k) for n >= 2.
[ "1", "1", "-8", "5", "126", "-168", "-2400", "4125", "50050", "-98098", "-1100736", "2339064", "25069968", "-56279520", "-585307008", "1367240589", "13919870250", "-33510798750", "-335813478000", "827780223270", "8194328596740", "-20587404077760", "-201822515032320", "515067876905400", "5009403008531376", "-12953308371172848" ]
[ "sign", "easy" ]
20
1
3
[ "A006480", "A361710", "A361711", "A361716" ]
null
Peter Bala, Mar 21 2023
2023-03-26T10:27:20
oeisdata/seq/A361/A361711.seq
bec3b7714381f369c1d72a53c23f8a36
A361712
a(n) = Sum_{k = 0..n-1} binomial(n,k)^2*binomial(n+k,k)*binomial(n+k-1,k).
[ "0", "1", "25", "649", "16921", "448751", "12160177", "336745053", "9513822745", "273585035755", "7988828082775", "236367018090017", "7072779699975601", "213701611408357567", "6511338458568750853", "199850727914988936149", "6173376842290368719385", "191776434791965521115235", "5987554996434696230487955" ]
[ "nonn", "easy" ]
35
0
3
[ "A005259", "A212334", "A361712", "A361713", "A361714", "A361715", "A361717", "A361877", "A361878" ]
null
Peter Bala, Mar 21 2023
2025-03-26T08:31:50
oeisdata/seq/A361/A361712.seq
2ab3430d2803c25a14c75d3bd706b946
A361713
a(n) = Sum_{k = 0..n-1} binomial(n,k)^2 * binomial(n+k-1,k)^2.
[ "0", "1", "17", "406", "10257", "268126", "7213166", "198978074", "5609330705", "161095277710", "4700175389142", "138986764820410", "4157185583199534", "125568602682092818", "3825026187780837266", "117376010145070696906", "3625095243230562818065", "112596592142021739522670", "3514965607470183733302470" ]
[ "nonn", "easy" ]
23
0
3
[ "A005259", "A060150", "A177316", "A212334", "A361712", "A361713", "A361714", "A361715", "A361717" ]
null
Peter Bala, Mar 21 2023
2024-07-11T05:11:06
oeisdata/seq/A361/A361713.seq
7de55ef4add99e6d3b28de0d45d2d652
A361714
a(n) = Sum_{k = 0..n-1} (-1)^(n+k+1)*binomial(n,k)*binomial(n+k-1,k)^2.
[ "0", "1", "7", "82", "1063", "14376", "199204", "2806770", "40053031", "577468684", "8397778882", "123029274666", "1814016998116", "26898142793068", "400836647993292", "5999796281063082", "90162110212198695", "1359731143731297396", "20571691450059355174", "312134224830052880826", "4748435338386591995938" ]
[ "nonn", "easy" ]
22
0
3
[ "A005258", "A352654", "A361712", "A361713", "A361714", "A361715", "A361717" ]
null
Peter Bala, Mar 21 2023
2024-07-11T05:11:21
oeisdata/seq/A361/A361714.seq
f44cd2286878e85194fc71d643b9d73f
A361715
a(n) = Sum_{k = 0..n-1} binomial(n,k)^2*binomial(n+k-1,k).
[ "0", "1", "9", "82", "745", "6876", "64764", "621860", "6070761", "60085720", "601493134", "6078225792", "61907445340", "634751002718", "6545478537810", "67830084149832", "705950951578089", "7375212511115184", "77310175072063914", "812839577957617640", "8569327793354169870", "90562666708303706642", "959212007563384494522", "10180245921386807485152" ]
[ "nonn", "easy" ]
15
0
3
[ "A005258", "A103882", "A361712", "A361713", "A361714", "A361715", "A361717" ]
null
Peter Bala, Mar 23 2023
2025-03-26T08:31:46
oeisdata/seq/A361/A361715.seq
5aec02bd01f4de81739559450d949b30
A361716
a(n) = Sum_{k = 0..n-1} (-1)^k*binomial(n,k)^2*binomial(n-1,k).
[ "0", "1", "-3", "-8", "45", "126", "-840", "-2400", "17325", "50050", "-378378", "-1100736", "8576568", "25069968", "-199536480", "-585307008", "4732755885", "13919870250", "-113936715750", "-335813478000", "2775498395670", "8194328596740", "-68263497731520", "-201822515032320" ]
[ "sign", "easy" ]
39
0
3
[ "A006480", "A245086", "A361710", "A361711", "A361716" ]
null
Peter Bala, Mar 23 2023
2023-10-06T09:28:26
oeisdata/seq/A361/A361716.seq
8aab48cca803bb93b7a676371aa6336e
A361717
a(n) = Sum_{k = 0..n-1} binomial(n-1,k)^2*binomial(n+k,k).
[ "0", "1", "4", "27", "216", "1875", "17088", "160867", "1549936", "15195843", "151017780", "1517232189", "15379549056", "157058738343", "1614039427224", "16676755365555", "173118505001952", "1804500885273123", "18877476988765404", "198120856336103017", "2085303730716475960" ]
[ "nonn", "easy" ]
32
0
3
[ "A005258", "A006480", "A060542", "A361712", "A361713", "A361714", "A361715", "A361717" ]
null
Peter Bala, Mar 26 2023
2024-10-12T21:33:58
oeisdata/seq/A361/A361717.seq
c59a63fa8518c821f5b0ceb602082c94
A361718
Triangular array read by rows. T(n,k) is the number of labeled directed acyclic graphs on [n] with exactly k nodes of indegree 0.
[ "1", "0", "1", "0", "2", "1", "0", "15", "9", "1", "0", "316", "198", "28", "1", "0", "16885", "10710", "1610", "75", "1", "0", "2174586", "1384335", "211820", "10575", "186", "1", "0", "654313415", "416990763", "64144675", "3268125", "61845", "441", "1", "0", "450179768312", "286992935964", "44218682312", "2266772550", "43832264", "336924", "1016", "1" ]
[ "nonn", "tabl" ]
28
0
5
[ "A000169", "A000612", "A003024", "A003025", "A003087", "A058876", "A058877", "A058891", "A059201", "A082402", "A088957", "A133686", "A134531", "A224069", "A323818", "A323819", "A334282", "A350415", "A361579", "A361718", "A367904", "A367908", "A368600", "A368601", "A368602" ]
null
Geoffrey Critzer, Apr 02 2023
2024-01-04T18:11:12
oeisdata/seq/A361/A361718.seq
1044a410536da723fc719de69a06c073
A361719
a(n) = Sum_{k = 1..n} (-1)^(n+k) * k^3 * binomial(n,k)^2.
[ "0", "1", "4", "-36", "-96", "450", "1080", "-3920", "-8960", "28350", "63000", "-182952", "-399168", "1093092", "2354352", "-6177600", "-13178880", "33474870", "70887960", "-175518200", "-369512000", "896251356", "1877859984", "-4478082336", "-9345563136", "21971267500", "45700236400", "-106148523600", "-220159900800" ]
[ "sign", "easy" ]
19
0
3
[ "A000984", "A001405", "A002117", "A294486", "A361719" ]
null
Peter Bala, Mar 24 2023
2023-11-03T07:12:18
oeisdata/seq/A361/A361719.seq
a58a9fe7153075792e58a8d3de61d46c
A361720
Number of nonisomorphic right involutory Płonka magmas with n elements.
[ "1", "1", "2", "4", "12", "37", "164", "849", "6081", "56164", "698921" ]
[ "nonn", "hard", "more" ]
66
0
3
[ "A000041", "A001329", "A361720", "A362382", "A362385", "A362642", "A362821", "A362822" ]
null
Philip Turecek, Apr 14 2023
2023-05-27T22:38:41
oeisdata/seq/A361/A361720.seq
ca398f446d1fab3054d1d4a7684953ef
A361721
a(n) = number of isogeny classes of p-divisible groups of abelian varieties of dimension n over an algebraically closed field of characteristic p (for any fixed prime p).
[ "1", "2", "3", "5", "8", "13", "20", "31", "47", "70", "103", "151", "218", "313", "446", "629", "883", "1233", "1711", "2362", "3244", "4433", "6034", "8179", "11043", "14852", "19906", "26589", "35400", "46986", "62182", "82057", "107989", "141744", "185583", "242387", "315842", "410627", "532687", "689573", "890837", "1148567", "1478020", "1898430", "2434006", "3115202", "3980232" ]
[ "nonn" ]
25
0
2
[ "A061255", "A361721" ]
null
Steven Groen, James Rawson, and Robin Visser, Mar 21 2023
2024-05-10T08:50:04
oeisdata/seq/A361/A361721.seq
c3177906dd42c9bc9875728e4065c521
A361722
Index of where prime(n) first appears as a divisor of any term in A359804.
[ "2", "3", "4", "8", "13", "31", "44", "47", "55", "66", "84", "96", "121", "125", "135", "143", "154", "161", "179", "192", "197", "218", "231", "242", "267", "270", "279", "293", "303", "308", "341", "352", "372", "379", "403", "412", "426", "440", "462", "476", "494", "501", "524", "530", "542", "545", "578", "617", "626", "639", "645", "665", "668", "697", "717", "730", "741", "748", "770", "786", "798", "822", "850" ]
[ "nonn" ]
7
1
1
[ "A359804", "A361502", "A361503", "A361504", "A361722" ]
null
Scott R. Shannon and N. J. A. Sloane, Mar 21 2023
2023-03-24T16:35:16
oeisdata/seq/A361/A361722.seq
5972d7027815539452e1de8fe713619d
A361723
Numbers k such that there are 18 primes between 100*k and 100*k + 99.
[ "1228537713709", "23352869714018", "28703237474266", "144785865481702", "161394923966449", "168975708209638", "174748809066898", "207552241231357", "278215179205531", "312303328909720", "592248982143877", "812939886634531", "939100782752014", "983930290209021", "1111161494544274" ]
[ "nonn" ]
47
1
1
[ "A038822", "A181098", "A186311", "A186393", "A186408", "A186509", "A261571", "A361723" ]
null
Brian Kehrig, Mar 21 2023
2024-05-19T11:50:21
oeisdata/seq/A361/A361723.seq
87192d4c10466dc0fc6c1bc0e76ce408
A361724
Lexicographically earliest sequence of distinct positive numbers on a square spiral such that the eight sums of each number with its eight nearest neighbors are distinct across the entire spiral and no number on the spiral equals any such sum.
[ "1", "2", "4", "7", "12", "14", "16", "22", "27", "10", "31", "40", "39", "46", "47", "20", "45", "52", "61", "60", "18", "80", "68", "81", "82", "70", "89", "94", "83", "48", "62", "105", "100", "69", "117", "25", "111", "129", "127", "124", "143", "106", "112", "132", "155", "119", "126", "128", "63", "56", "157", "158", "107", "178", "193", "168", "118", "170", "55", "195", "189", "197", "192", "206", "182", "211", "202" ]
[ "nonn", "look" ]
13
1
2
[ "A174344", "A274640", "A274923", "A307834", "A355270", "A358151", "A361724" ]
null
Scott R. Shannon and Eric Angelini, Mar 22 2023
2023-03-22T08:06:27
oeisdata/seq/A361/A361724.seq
8dad6fd4698a593770bf2233da59d337
A361725
a(n) is the largest of two middle prime factors of n if the number of primes divisors counted with multiplicity (A001222(n)) is even, otherwise is the middle prime factor of n.
[ "2", "3", "2", "5", "3", "7", "2", "3", "5", "11", "2", "13", "7", "5", "2", "17", "3", "19", "2", "7", "11", "23", "2", "5", "13", "3", "2", "29", "3", "31", "2", "11", "17", "7", "3", "37", "19", "13", "2", "41", "3", "43", "2", "3", "23", "47", "2", "7", "5", "17", "2", "53", "3", "11", "2", "19", "29", "59", "3", "61", "31", "3", "2", "13", "3", "67", "2", "23", "5", "71", "2", "73", "37", "5", "2", "11", "3" ]
[ "nonn" ]
15
2
1
[ "A001222", "A027746", "A079879", "A361632", "A361633", "A361725" ]
null
Stefano Spezia, Mar 22 2023
2023-03-24T08:41:46
oeisdata/seq/A361/A361725.seq
933bc4d4cd636f98f10ac024e481908c
A361726
Diagonal of rational function 1/(1 - (1 + x*y) * (x^2 + y^2)).
[ "1", "0", "2", "4", "8", "24", "56", "144", "376", "960", "2512", "6560", "17184", "45248", "119296", "315392", "835552", "2217216", "5893568", "15687552", "41810944", "111567104", "298016512", "796832256", "2132456704", "5711486976", "15309014528", "41062927360", "110213725184", "295995574272", "795391639552" ]
[ "nonn" ]
23
0
3
[ "A115962", "A137635", "A360266", "A361726", "A361727" ]
null
Seiichi Manyama, Mar 22 2023
2023-03-23T16:45:34
oeisdata/seq/A361/A361726.seq
3a9d2238990a4c2cbcac28d2e10cb646
A361727
Diagonal of rational function 1/(1 - (1 + x*y) * (x^3 + y^3)).
[ "1", "0", "0", "2", "4", "2", "6", "24", "36", "44", "126", "300", "470", "860", "2080", "4192", "7420", "15260", "33124", "64568", "124558", "259632", "535668", "1055460", "2118414", "4373412", "8872644", "17765396", "36138168", "73972404", "149793424", "303140552", "618565948", "1261454064", "2561056212", "5211145368" ]
[ "nonn" ]
15
0
4
[ "A137635", "A361726", "A361727" ]
null
Seiichi Manyama, Mar 22 2023
2023-03-22T12:48:29
oeisdata/seq/A361/A361727.seq
a1a0419bf6cd99217e69274dec384d1c
A361728
Diagonal of rational function 1/(1 - (1 + x*y*z) * (x + y + z)).
[ "1", "6", "108", "2238", "51126", "1234836", "30933846", "795124008", "20832161238", "553908550416", "14901620938668", "404737904238768", "11080360585597974", "305375448989901564", "8464333256181647028", "235772833122673888788", "6595763835075158604618" ]
[ "nonn" ]
15
0
2
[ "A361728", "A361729", "A361730" ]
null
Seiichi Manyama, Mar 22 2023
2024-03-17T08:41:58
oeisdata/seq/A361/A361728.seq
d16ee1cd067a6058947ee3e153bfdd92
A361729
Diagonal of rational function 1/(1 - (1 + x*y*z) * (x^2 + y^2 + z^2)).
[ "1", "0", "6", "18", "108", "546", "3030", "16920", "96480", "557460", "3255426", "19186020", "113905386", "680583708", "4088506428", "24677473884", "149564145060", "909784736388", "5552109174084", "33981183515664", "208523253915306", "1282621025382840", "7906367632595328", "48832556909752044" ]
[ "nonn" ]
20
0
3
[ "A361728", "A361729", "A361730" ]
null
Seiichi Manyama, Mar 22 2023
2024-03-17T08:42:43
oeisdata/seq/A361/A361729.seq
3e8872385f6f32d90817f18d1b4879a1
A361730
Diagonal of rational function 1/(1 - (1 + x*y*z) * (x^3 + y^3 + z^3)).
[ "1", "0", "0", "6", "18", "18", "96", "540", "1350", "3480", "16470", "61020", "175860", "627480", "2498580", "8520876", "28563570", "106917300", "393495396", "1369171188", "4914119826", "18191218716", "65741140080", "235643531508", "862450963704", "3163777886412", "11484836808588", "41875694151720" ]
[ "nonn" ]
16
0
4
[ "A115055", "A361728", "A361729", "A361730" ]
null
Seiichi Manyama, Mar 22 2023
2023-03-22T12:28:20
oeisdata/seq/A361/A361730.seq
2a4785b0d0a97b80f6948a769f3e4a7d
A361731
Array read by descending antidiagonals. A(n, k) = hypergeom([-k, -3], [1], n).
[ "1", "1", "1", "1", "4", "1", "1", "10", "7", "1", "1", "20", "25", "10", "1", "1", "35", "63", "46", "13", "1", "1", "56", "129", "136", "73", "16", "1", "1", "84", "231", "307", "245", "106", "19", "1", "1", "120", "377", "586", "593", "396", "145", "22", "1", "1", "165", "575", "1000", "1181", "1011", "595", "190", "25", "1", "1", "220", "833", "1576", "2073", "2076", "1585", "848", "241", "28", "1" ]
[ "nonn", "tabl" ]
8
0
5
[ "A000012", "A000292", "A001845", "A016777", "A077028", "A081583", "A081586", "A081588", "A081590", "A100536", "A361682", "A361731" ]
null
Peter Luschny, Mar 22 2023
2023-03-23T07:57:42
oeisdata/seq/A361/A361731.seq
e391cf7f2bf3e565aca0e86105e8a0b9
A361732
a(n) = [x^n] (x^5 + 5*x^4 + 4*x^3 - 3*x + 1)/(x^2 + 2*x - 1)^2.
[ "1", "1", "2", "6", "20", "60", "174", "490", "1352", "3672", "9850", "26158", "68892", "180180", "468454", "1211730", "3120400", "8004144", "20460402", "52139990", "132502180", "335882988", "849507230", "2144114234", "5401408344", "13583493000", "34105191146", "85504030974", "214070361260", "535269125508", "1336814464470" ]
[ "nonn" ]
17
0
3
[ "A000129", "A361732", "A361758" ]
null
Peter Luschny, Mar 23 2023
2025-03-26T08:31:55
oeisdata/seq/A361/A361732.seq
6067d80796dee8b581135e5794f8eb13
A361733
Length of the Collatz (3x + 1) trajectory from k = 10^n - 1 to a term less than k, or -1 if the trajectory never goes below k.
[ "4", "7", "17", "12", "113", "17", "79", "22", "51", "33", "64", "35", "128", "56", "110", "53", "84", "128", "107", "115", "175", "82", "477", "172", "141", "182", "188", "110", "159", "167", "301", "206", "151", "146", "128", "195", "190", "299", "208", "276", "180", "185", "500", "203", "229", "190", "265", "270", "288", "252", "299", "208", "350", "348", "459", "330", "314", "268", "490", "361", "578" ]
[ "nonn" ]
61
1
1
[ "A002283", "A006370", "A074473", "A074474", "A075480", "A075483", "A361733" ]
null
Paul M. Bradley, Mar 22 2023
2023-05-13T13:45:50
oeisdata/seq/A361/A361733.seq
e8e18d0efd5987fb8522173ebce73bc9
A361734
Semi-Padovan sequence: a(2*n) = a(n) and a(2*n+1) = a(2*n-1) + a(2*n-2), with a(0) = 1 and a(1) = 0.
[ "1", "0", "0", "1", "0", "1", "1", "1", "0", "2", "1", "2", "1", "3", "1", "4", "0", "5", "2", "5", "1", "7", "2", "8", "1", "10", "3", "11", "1", "14", "4", "15", "0", "19", "5", "19", "2", "24", "5", "26", "1", "31", "7", "32", "2", "39", "8", "41", "1", "49", "10", "50", "3", "60", "11", "63", "1", "74", "14", "75", "4", "89", "15", "93", "0", "108", "19", "108", "5", "127", "19", "132", "2", "151", "24", "153", "5", "177", "26", "182", "1" ]
[ "nonn" ]
18
0
10
[ "A000079", "A361734", "A361735", "A361736" ]
null
Michel Marcus, Mar 22 2023
2023-03-23T07:57:22
oeisdata/seq/A361/A361734.seq
893ff3da2af02434d4af97b61d3faae5
A361735
Modified semi-Padovan sequence: a(2*n) = a(n) and a(2*n+1) = a(2*n-1) + a(2*n-2), with a(0) = 0 and a(1) = 1.
[ "0", "1", "1", "1", "1", "2", "1", "3", "1", "4", "2", "5", "1", "7", "3", "8", "1", "11", "4", "12", "2", "16", "5", "18", "1", "23", "7", "24", "3", "31", "8", "34", "1", "42", "11", "43", "4", "54", "12", "58", "2", "70", "16", "72", "5", "88", "18", "93", "1", "111", "23", "112", "7", "135", "24", "142", "3", "166", "31", "169", "8", "200", "34", "208", "1", "242", "42", "243", "11", "285", "43" ]
[ "nonn" ]
14
0
6
[ "A361734", "A361735", "A361736" ]
null
Michel Marcus, Mar 22 2023
2023-03-22T22:00:56
oeisdata/seq/A361/A361735.seq
62d0ea1b8cddaca5ee95e3b56df9321a
A361736
Semi-Lucas sequence: a(2*n) = a(n) and a(2*n+1) = a(2*n) + a(2*n-1), with a(1) = 2 and a(2) = 1.
[ "2", "1", "3", "1", "4", "3", "7", "1", "8", "4", "12", "3", "15", "7", "22", "1", "23", "8", "31", "4", "35", "12", "47", "3", "50", "15", "65", "7", "72", "22", "94", "1", "95", "23", "118", "8", "126", "31", "157", "4", "161", "35", "196", "12", "208", "47", "255", "3", "258", "50", "308", "15", "323", "65", "388", "7", "395", "72", "467", "22", "489", "94", "583", "1", "584", "95", "679", "23", "702", "118" ]
[ "nonn" ]
12
1
1
[ "A361734", "A361735", "A361736" ]
null
Michel Marcus, Mar 22 2023
2023-03-22T22:01:05
oeisdata/seq/A361/A361736.seq
04f1d404590a48a429c20305d2578e17
A361737
Diagonal of rational function 1/(1 - (x + y + z + x^2*y*z)).
[ "1", "6", "96", "1860", "39780", "900396", "21146496", "509697936", "12523921740", "312324904320", "7881117611796", "200784546041976", "5156135919980136", "133299228503087640", "3465901878247744920", "90563401722349627920", "2376642701449937741580", "62607393746503658100360" ]
[ "nonn" ]
11
0
2
[ "A361728", "A361737", "A361738", "A361739" ]
null
Seiichi Manyama, Mar 22 2023
2023-03-23T05:31:57
oeisdata/seq/A361/A361737.seq
5aad00161f0644ed031fb3ddec8fde15
A361738
Diagonal of rational function 1/(1 - (x^2 + y^2 + z^2 + x^3*y*z)).
[ "1", "0", "6", "6", "90", "180", "1770", "5040", "39690", "140280", "964656", "3922380", "24755346", "110486376", "660153780", "3137330196", "18103340970", "89794566576", "506892467796", "2589310074780", "14419819659960", "75181803891480", "415298937771900", "2196704341517400", "12078576672927570" ]
[ "nonn" ]
16
0
3
[ "A361729", "A361737", "A361738", "A361739" ]
null
Seiichi Manyama, Mar 22 2023
2023-03-23T15:31:43
oeisdata/seq/A361/A361738.seq
e44198b2defa81859c693c3c07ad8fc0
A361739
Diagonal of rational function 1/(1 - (x^3 + y^3 + z^3 + x^4*y*z)).
[ "1", "0", "0", "6", "6", "0", "90", "180", "90", "1680", "5040", "5040", "36330", "138600", "207900", "895356", "3818430", "7567560", "24720696", "106702596", "258053796", "742135680", "3050807760", "8483450976", "23450218506", "89691647760", "273414861720", "760735601340", "2713845780360", "8733512193120", "24957399366900" ]
[ "nonn" ]
15
0
4
[ "A361730", "A361737", "A361738", "A361739" ]
null
Seiichi Manyama, Mar 22 2023
2023-03-23T06:48:20
oeisdata/seq/A361/A361739.seq
7fb9ec0e613c5be55ac457b8c7a0c2e1
A361740
Right border of A362312.
[ "0", "2", "1", "4", "3", "6", "5", "9", "7", "8", "11", "10", "13", "12", "15", "16", "14", "18", "17", "20", "19", "22", "21", "24", "23", "26", "25", "28", "27", "30", "29", "32", "31", "34", "33", "36", "35", "38", "37", "40", "39", "42", "41", "44", "43", "46", "45", "48", "47", "50", "49", "52", "51", "54", "53", "56", "55", "58", "57", "60", "59", "62", "61", "64", "63", "66", "65", "68" ]
[ "nonn" ]
26
0
2
[ "A361740", "A362312" ]
null
Rémy Sigrist, Apr 16 2023
2023-04-17T15:23:18
oeisdata/seq/A361/A361740.seq
a910dee106c7f44a850612298eb9ab1b
A361741
Starting positions of digit triples in the decimal expansion of Pi where the sum of the first 2 equals the third.
[ "1", "3", "10", "29", "61", "73", "83", "106", "117", "132", "177", "192", "195", "198", "241", "248", "251", "281", "309", "311", "333", "362", "381", "393", "432", "477", "486", "494", "504", "508", "525", "532", "536", "555", "602", "611", "628", "647", "662", "674", "689", "699", "710", "747", "755", "760", "771", "806", "853", "856", "887", "899", "927", "934", "966", "969", "989" ]
[ "nonn", "base" ]
66
1
2
[ "A000796", "A110883", "A361741" ]
null
Aaron T Cowan, Mar 22 2023
2023-05-02T13:56:13
oeisdata/seq/A361/A361741.seq
470aa4998910a36dbcdf8b27b7ff353a
A361742
Lexicographically earliest sequence of nonnegative integers such that for any distinct m and n, the m X m square with lower left corner at (m, a(m)) and the n X n square with lower left corner at (n, a(n)) do not overlap (they can however touch).
[ "0", "0", "2", "5", "9", "14", "20", "0", "27", "36", "46", "8", "57", "70", "84", "99", "115", "132", "150", "20", "169", "190", "212", "235", "259", "40", "284", "311", "339", "66", "368", "399", "431", "96", "464", "499", "535", "130", "572", "0", "611", "652", "694", "168", "737", "782", "828", "875", "923", "212", "972", "1023", "1075", "1128", "1182", "262", "1237" ]
[ "nonn" ]
14
1
3
[ "A000217", "A289523", "A361697", "A361742" ]
null
Rémy Sigrist, Mar 22 2023
2023-04-10T06:50:24
oeisdata/seq/A361/A361742.seq
1a5324c765c44ab6557169f893104d10
A361743
Central circular Delannoy numbers: a(n) is the number of Delannoy loops on an n X n toroidal grid.
[ "1", "2", "16", "114", "768", "5010", "32016", "201698", "1257472", "7777314", "47800080", "292292946", "1779856128", "10799942322", "65336473104", "394246725570", "2373580947456", "14262064668738", "85546366040592", "512323096241714", "3063932437123840", "18300660294266322", "109183694129335056" ]
[ "nonn" ]
41
0
2
[ "A001850", "A002003", "A008288", "A047781", "A108666", "A361743", "A361745" ]
null
Noah Snyder, Mar 22 2023
2023-03-23T05:09:03
oeisdata/seq/A361/A361743.seq
70864e5ce3b5052cc59d7a5389954088
A361744
A(n,k) is the least m such that there are k primes in the set {prime(n) + 2^i | 1 <= i <= m}, or -1 if no such number exists; square array A(n,k), n > 1, k >= 1, read by antidiagonals.
[ "1", "2", "1", "3", "3", "2", "4", "5", "4", "1", "6", "11", "6", "3", "2", "7", "47", "8", "5", "4", "1", "12", "53", "10", "7", "8", "13", "2", "15", "141", "16", "9", "20", "21", "6", "3", "16", "143", "18", "15", "38", "33", "30", "7", "1", "18", "191", "20", "23", "64", "81", "162", "39", "3", "4", "28", "273", "28", "29", "80", "129", "654", "79", "5", "12", "2" ]
[ "nonn", "tabl" ]
60
2
2
[ "A019434", "A057195", "A057196", "A057197", "A057200", "A057201", "A057203", "A057221", "A057732", "A059242", "A094076", "A102633", "A102634", "A205558", "A231232", "A361679", "A361744" ]
null
Jean-Marc Rebert, Mar 22 2023
2023-04-07T09:24:39
oeisdata/seq/A361/A361744.seq
228442a4636fa1d0da793b3e341c4201
A361745
Square array of circular Delannoy numbers A(i,j) (i >= 0, j >= 0) read by antidiagonals.
[ "1", "1", "1", "1", "2", "1", "1", "4", "4", "1", "1", "6", "16", "6", "1", "1", "8", "36", "36", "8", "1", "1", "10", "64", "114", "64", "10", "1", "1", "12", "100", "264", "264", "100", "12", "1", "1", "14", "144", "510", "768", "510", "144", "14", "1", "1", "16", "196", "876", "1800", "1800", "876", "196", "16", "1", "1", "18", "256", "1386", "3648", "5010", "3648", "1386", "256", "18", "1" ]
[ "nonn", "tabl" ]
25
0
5
[ "A008288", "A104698", "A142978", "A361743", "A361745", "A361758" ]
null
Noah Snyder, Mar 22 2023
2023-03-24T02:55:26
oeisdata/seq/A361/A361745.seq
10d2b754620bd49587e75405bc66cab5
A361746
Number of occurrences of the most frequently occurring letter(s) in US English name of n.
[ "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "3", "2", "2", "2", "2", "2", "4", "3", "3", "2", "2", "3", "3", "2", "2", "2", "3", "3", "3", "2", "2", "3", "3", "2", "2", "2", "2", "3", "2", "1", "2", "2", "2", "2", "2", "1", "2", "2", "2", "2", "2", "2", "2", "3", "3", "2", "2", "2", "2", "1", "1", "2", "2", "1", "2", "2", "2", "2", "2", "2", "3", "2", "4", "2", "3", "2", "4", "3", "3", "1", "2", "2", "3", "1", "2", "2", "3", "2", "2", "2", "3", "2", "3", "2", "2", "2", "3", "2", "4", "2" ]
[ "easy", "nonn", "word", "less" ]
22
0
4
[ "A005589", "A361746" ]
null
James C. McMahon, Mar 22 2023
2023-03-26T11:33:29
oeisdata/seq/A361/A361746.seq
bf8752b8bf5578cc50086782631498ab
A361747
Lexicographically earliest sequence of distinct positive integers such that a(n) and a(n-1) share at least one identical trit at the same position in their balanced ternary representations.
[ "1", "4", "2", "3", "6", "5", "7", "8", "9", "10", "11", "12", "13", "16", "14", "15", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "43", "41", "42", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67" ]
[ "base", "nonn" ]
8
1
2
null
null
Jodi Spitz, Mar 22 2023
2023-03-24T18:00:50
oeisdata/seq/A361/A361747.seq
cfd4f3a6ce6e8ca711827fece91ae075
A361748
Triangle T(n, k) of distinct positive integers, n > 0, k = 1..n, read by rows and filled in the greedy way such that T(n, k) is a multiple of T(n, 1).
[ "1", "2", "4", "3", "6", "9", "5", "10", "15", "20", "7", "14", "21", "28", "35", "8", "16", "24", "32", "40", "48", "11", "22", "33", "44", "55", "66", "77", "12", "36", "60", "72", "84", "96", "108", "120", "13", "26", "39", "52", "65", "78", "91", "104", "117", "17", "34", "51", "68", "85", "102", "119", "136", "153", "170", "18", "54", "90", "126", "144", "162", "180", "198", "216", "234", "252" ]
[ "nonn", "tabl", "easy" ]
69
1
2
[ "A360371", "A361748", "A361939" ]
null
Rémy Sigrist, Mar 30 2023
2023-04-03T10:21:37
oeisdata/seq/A361/A361748.seq
2308d33dd7868ce2125aa839bf3cd711
A361749
a(n) is the number of n X n matrices with nonnegative integer entries, row sums 1,2,...,n and column sums 1,2,...,n.
[ "1", "1", "2", "12", "261", "22645", "8264346", "13150070522", "93589674933872", "3036609755945925595", "455845471095088280120142", "320342093420041869298750385976", "1063978124653925432733949863518874116", "16835366182312565093823092118182447742597067" ]
[ "nonn" ]
18
0
3
[ "A000681", "A110058", "A361749" ]
null
Robert Israel, Mar 23 2023
2023-06-26T09:40:30
oeisdata/seq/A361/A361749.seq
ec4fc16362192f1bf453cc293526a266
A361750
Terms of A329150 that have several preimages.
[ "23", "223", "230", "232", "233", "235", "237", "323", "523", "723", "1123", "1323", "1723", "1923", "2023", "2223", "2230", "2232", "2233", "2235", "2237", "2300", "2302", "2303", "2305", "2307", "2311", "2313", "2317", "2319", "2320", "2322", "2323", "2325", "2327", "2330", "2332", "2333", "2335", "2337", "2350", "2352", "2353", "2355", "2357", "2370", "2372", "2373", "2375", "2377" ]
[ "nonn", "base" ]
24
1
1
[ "A329147", "A329149", "A329150", "A361750" ]
null
Bernard Schott, Mar 23 2023
2023-03-24T17:14:30
oeisdata/seq/A361/A361750.seq
4e308d08a39d407a7b7d065fc4ff195c
A361751
a(n) is the number of decimal digits in A098129(n) and A300517(n).
[ "1", "3", "6", "10", "15", "21", "28", "36", "45", "65", "87", "111", "137", "165", "195", "227", "261", "297", "335", "375", "417", "461", "507", "555", "605", "657", "711", "767", "825", "885", "947", "1011", "1077", "1145", "1215", "1287", "1361", "1437", "1515", "1595", "1677", "1761", "1847", "1935", "2025", "2117", "2211", "2307", "2405", "2505", "2607", "2711", "2817", "2925" ]
[ "nonn", "base", "easy" ]
70
1
2
[ "A055642", "A098129", "A110803", "A300517", "A361751" ]
null
David Cleaver, Mar 23 2023
2023-04-15T06:27:21
oeisdata/seq/A361/A361751.seq
861dcd4a11ad2586fa8b74dc45078e0c
A361752
a(n) = Sum_{k=0..floor(n/2)} binomial(2*(n-2*k),k) * binomial(2*(n-2*k),n-2*k).
[ "1", "2", "6", "24", "94", "374", "1520", "6252", "25942", "108408", "455586", "1923444", "8151856", "34661252", "147788484", "631660788", "2705471254", "11609393084", "49899207640", "214792704256", "925811868178", "3995288307392", "17260287754284", "74641620619072", "323080683587056", "1399606566298916" ]
[ "nonn" ]
20
0
2
[ "A137635", "A360266", "A361752", "A361753" ]
null
Seiichi Manyama, Mar 23 2023
2023-03-23T19:31:03
oeisdata/seq/A361/A361752.seq
5a923319b3e4f2f8c78c0320381b4551
A361753
a(n) = Sum_{k=0..floor(n/3)} binomial(2*(n-3*k),k) * binomial(2*(n-3*k),n-3*k).
[ "1", "2", "6", "20", "74", "276", "1044", "3994", "15426", "60008", "234764", "922716", "3640700", "14411952", "57210750", "227659704", "907853778", "3627085932", "14515139376", "58174092472", "233463067284", "938061587212", "3773298437204", "15193083455580", "61230698571372", "246978403761112" ]
[ "nonn" ]
17
0
2
[ "A137635", "A360267", "A361752", "A361753" ]
null
Seiichi Manyama, Mar 23 2023
2023-03-23T19:32:11
oeisdata/seq/A361/A361753.seq
59fe3bbdc11c4adf879402f49863c961
A361754
The number of free polyominoes of area n that fill their minimal enclosing circle (MEC). A polyomino "fills" its minimal enclosing circle if no square may be added to it that doesn't have some point outside of the circle.
[ "1", "1", "0", "1", "1", "2", "1", "1", "1", "1", "1", "3", "2", "2", "2", "3", "2", "3", "1", "3", "2", "4", "1" ]
[ "nonn", "more" ]
13
1
6
[ "A147680", "A361754" ]
null
John Mason and Allan C. Wechsler, Mar 23 2023
2023-08-01T15:37:42
oeisdata/seq/A361/A361754.seq
3d3cf6bb7de43392395ea7f10ea89638
A361755
Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the Zeckendorf representation of k also appear in that of n.
[ "0", "0", "1", "0", "2", "0", "3", "0", "1", "3", "4", "0", "5", "0", "1", "5", "6", "0", "2", "5", "7", "0", "8", "0", "1", "8", "9", "0", "2", "8", "10", "0", "3", "8", "11", "0", "1", "3", "4", "8", "9", "11", "12", "0", "13", "0", "1", "13", "14", "0", "2", "13", "15", "0", "3", "13", "16", "0", "1", "3", "4", "13", "14", "16", "17", "0", "5", "13", "18", "0", "1", "5", "6", "13", "14", "18", "19", "0", "2", "5", "7", "13", "15", "18", "20" ]
[ "nonn", "tabf", "base" ]
13
0
5
[ "A003714", "A007895", "A139764", "A295989", "A356771", "A361755", "A361756" ]
null
Rémy Sigrist, Mar 23 2023
2023-03-27T03:42:47
oeisdata/seq/A361/A361755.seq
8a65509f7ce774c9cbc52563499bbb49
A361756
Irregular triangle T(n, k), n >= 0, k = 1..A361757(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the dual Zeckendorf representation of k also appear in that of n.
[ "0", "0", "1", "0", "2", "0", "1", "2", "3", "0", "1", "4", "0", "2", "5", "0", "1", "2", "3", "4", "5", "6", "0", "2", "7", "0", "1", "2", "3", "7", "8", "0", "1", "4", "9", "0", "2", "5", "7", "10", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "0", "1", "4", "12", "0", "2", "5", "13", "0", "1", "2", "3", "4", "5", "6", "12", "13", "14", "0", "2", "7", "15", "0", "1", "2", "3", "7", "8", "15", "16" ]
[ "nonn", "base", "tabf" ]
14
0
5
[ "A003754", "A003842", "A356771", "A361755", "A361756", "A361757" ]
null
Rémy Sigrist, Mar 23 2023
2023-03-27T03:42:43
oeisdata/seq/A361/A361756.seq
e7992eccb11b6b73e29e219fa12153a3
A361757
a(n) is the number of terms in the n-th row of A361756.
[ "1", "2", "2", "4", "3", "3", "7", "3", "6", "4", "5", "12", "4", "4", "10", "4", "8", "6", "8", "20", "4", "8", "5", "7", "17", "5", "5", "13", "6", "12", "9", "13", "33", "5", "5", "13", "5", "10", "8", "11", "28", "5", "10", "6", "9", "22", "7", "7", "19", "9", "18", "14", "21", "54", "5", "10", "6", "9", "22", "6", "6", "16", "8", "16", "12", "18", "46", "6", "6", "16", "6", "12", "10", "14", "36", "7" ]
[ "nonn", "base" ]
11
0
2
[ "A001911", "A112310", "A361756", "A361757" ]
null
Rémy Sigrist, Mar 23 2023
2023-03-27T03:42:40
oeisdata/seq/A361/A361757.seq
cf59b042c53e47967cc291ddacc05b57
A361758
a(n) = [x^n] (x^5 + 5*x^4 + 4*x^3 - 3*x + 1)/((1 - x)*(x^2 + 2*x - 1)^2).
[ "1", "2", "4", "10", "30", "90", "264", "754", "2106", "5778", "15628", "41786", "110678", "290858", "759312", "1971042", "5091442", "13095586", "33555988", "85695978", "218198158", "554081146", "1403588376", "3547702610", "8949110954", "22532603954", "56637795100", "142141826074", "356212187334", "891481312842" ]
[ "nonn" ]
4
0
2
[ "A361745", "A361758" ]
null
Peter Luschny, Mar 23 2023
2023-03-23T16:53:27
oeisdata/seq/A361/A361758.seq
bc1666e8e118990601a6272e01eeb0b3
A361759
Sum of b(i) where the first b terms are all k digits of n, followed by Keith-like sum of the previous k digits until b(i) >= n
[ "34", "33", "32", "44", "33", "40", "47", "54", "61", "39", "68", "75", "66", "86", "64", "76", "88", "100", "66", "73", "102", "96", "129", "99", "119", "139", "96", "108", "120", "132", "136", "117", "150", "112", "132", "152", "172", "116", "128", "140", "170", "138", "171", "204", "145", "165", "185", "205", "225", "148", "204", "159", "192", "225", "258", "178" ]
[ "nonn", "base" ]
17
10
1
[ "A007629", "A361759" ]
null
Diego V. G. Silva, Mar 23 2023
2023-03-26T11:36:10
oeisdata/seq/A361/A361759.seq
959cb4b3cb46a6ed9c45df4a30abf243
A361760
a(n) = Product_{i=prime(n)..prime(n+1)-1} i.
[ "2", "12", "30", "5040", "132", "43680", "306", "175560", "271252800", "870", "1402410240", "2193360", "1722", "3916440", "14658134400", "29142257760", "3540", "65418312960", "22005480", "5112", "184933148400", "41977440", "390190489920", "5346472978828800", "94109400", "10302", "119224560", "11556", "149059680", "120140035685601494718355200000", "272613120" ]
[ "nonn" ]
27
1
1
[ "A061214", "A072472", "A361760", "A361761" ]
null
Karl-Heinz Hofmann, Mar 23 2023
2023-04-16T15:55:35
oeisdata/seq/A361/A361760.seq
3581e6b97f225d573d6d7c2d84f9059d
A361761
a(n) = Product_{i=prime(n)..prime(n+1)} i.
[ "6", "60", "210", "55440", "1716", "742560", "5814", "4037880", "7866331200", "26970", "51889178880", "89927760", "74046", "184072680", "776881123200", "1719393207840", "215940", "4383026968320", "1562389080", "373176", "14609718723600", "3484127520", "34726953602880", "518607878946393600", "9505049400", "1061106" ]
[ "nonn" ]
25
1
1
[ "A006094", "A061214", "A072472", "A112231", "A361760", "A361761" ]
null
Karl-Heinz Hofmann, Mar 23 2023
2023-04-16T15:55:31
oeisdata/seq/A361/A361761.seq
6c1c97b20f82a5c705967cad0cc77c51
A361762
Expansion of g.f. A(x) satisfying A(x)^3 = A( x^3/(1 - 3*x)^3 ) / (1 - 3*x).
[ "1", "1", "2", "5", "15", "52", "197", "779", "3135", "12709", "51757", "211761", "871022", "3603282", "14992067", "62719588", "263724900", "1114107925", "4726879206", "20135644606", "86099626270", "369492052236", "1591170063412", "6875211016868", "29803706856996", "129607445296468", "565362988510604", "2473576310166981" ]
[ "nonn" ]
25
0
3
[ "A000108", "A361762", "A361763", "A361764" ]
null
Paul D. Hanna, Mar 23 2023
2023-03-25T14:13:43
oeisdata/seq/A361/A361762.seq
5f3ab544507643d30a31f003a2c3e7f3
A361763
Expansion of g.f. A(x) satisfying A(x)^3 = A( x^3/(1 - 3*x)^3 ).
[ "1", "3", "9", "28", "93", "333", "1271", "5064", "20673", "85460", "355659", "1486719", "6238608", "26278281", "111114558", "471608944", "2008906581", "8586410085", "36816550550", "158332335279", "682843960665", "2952865525730", "12802463157570", "55646477022330", "242465061290160", "1059022767175173", "4636452916770489" ]
[ "nonn" ]
34
1
2
[ "A091190", "A107092", "A264228", "A264229", "A264230", "A361762", "A361763", "A361765" ]
null
Paul D. Hanna, Mar 23 2023
2023-03-29T08:57:27
oeisdata/seq/A361/A361763.seq
34f22c3043c0a1a852ef8ca1902e08cc
A361764
Expansion of g.f. A(x) satisfying A(x)^5 = A( x^5/(1 - 5*x)^5 ) / (1 - 5*x).
[ "1", "1", "3", "11", "44", "185", "806", "3627", "16926", "82615", "425633", "2325804", "13438568", "81258283", "507109592", "3223435416", "20655599675", "132496854084", "847152571284", "5386490329194", "34026141582719", "213512516149309", "1331393810596499", "8255968489237781", "50955585198416275", "313329163267012645" ]
[ "nonn" ]
11
0
3
[ "A000108", "A091200", "A361762", "A361764", "A361765" ]
null
Paul D. Hanna, Mar 24 2023
2023-03-25T13:20:05
oeisdata/seq/A361/A361764.seq
632aec7f0169b0b556206d9d2c1b964c
A361765
Expansion of g.f. A(x) satisfying A(x)^5 = A( x^5/(1 - 5*x)^5 ).
[ "1", "5", "25", "125", "625", "3126", "15655", "78650", "397625", "2031875", "10553128", "56047040", "306020575", "1723544750", "10015548750", "59871903136", "366244516505", "2278239803025", "14324961668875", "90586470006875", "573925269278169", "3633524853973370", "22949197586894725", "144473478898021750" ]
[ "nonn" ]
15
1
2
[ "A352704", "A361763", "A361764", "A361765" ]
null
Paul D. Hanna, Mar 24 2023
2023-04-17T22:15:08
oeisdata/seq/A361/A361765.seq
69dc0ed6c358051179ebfc168cca18ca
A361766
Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * (1 - x^n/A(-x))^(n+2).
[ "1", "1", "2", "5", "12", "27", "57", "123", "280", "666", "1614", "3955", "9733", "23949", "58967", "145844", "363137", "910339", "2295192", "5811070", "14754567", "37542078", "95715596", "244567665", "626388406", "1608131393", "4137707994", "10667045757", "27546269363", "71241831762", "184508259405", "478501423792" ]
[ "nonn" ]
15
0
3
[ "A355866", "A358952", "A361766" ]
null
Paul D. Hanna, Mar 26 2023
2025-01-21T22:20:28
oeisdata/seq/A361/A361766.seq
6c920c8488ba0ace95db1973dbe8a275
A361767
Expansion of e.g.f. A(x) = 1/F(oo,x) where F(oo,x) is the limit of the process F(n,x) = (F(n-1,x)^n - x^n)^(1/n) for n > 0, starting with F(0,x) = 1.
[ "1", "1", "3", "17", "143", "1599", "22369", "376417", "7409793", "167120657", "4249941371", "120323916591", "3753781567183", "127950507522967", "4731189132093033", "188631199008696389", "8066710048305641729", "368331028066068082977", "17885422396274431047283", "920319838571287315515007", "50024628127300451995229871" ]
[ "nonn" ]
17
0
3
[ "A361767", "A361768" ]
null
Paul D. Hanna, Mar 29 2023
2023-04-07T16:57:14
oeisdata/seq/A361/A361767.seq
64ed45a2e1da9d13319dba03099e5cbf
A361768
Expansion of o.g.f. A(x) = 1/F(oo,x) where F(oo,x) is the limit of the process F(n,x) = (F(n-1,x)^n - n^2*x^n)^(1/n) for n > 0, starting with F(0,x) = 1.
[ "1", "1", "3", "10", "35", "130", "499", "1966", "7893", "32168", "132690", "552784", "2322094", "9823572", "41811597", "178903031", "769044018", "3319438968", "14380154747", "62500478960", "272448124262", "1190815525727", "5217483053052", "22910925764270", "100811396881651", "444418225515884", "1962579128519888" ]
[ "nonn" ]
12
0
3
[ "A361767", "A361768", "A361769" ]
null
Paul D. Hanna, Mar 29 2023
2023-04-07T16:57:34
oeisdata/seq/A361/A361768.seq
0f59aff815aac4fe589f56b444cc8bdd
A361769
Expansion of g.f. A(x) = 1/F(oo,x) where F(oo,x) is the limit of the process F(n,x) = (F(n-1,x)^(2^n) - 4^n*x^n)^(1/2^n) for n > 0, starting with F(0,x) = 1.
[ "1", "2", "10", "68", "550", "5100", "53668", "644328", "9018182", "153030092", "3321466604", "97297000440", "3981224972764", "229643688537720", "18585336250711944", "2096852727301094224", "328430095865115148102", "71267322442955095825676", "21402682985817534443455388", "8892250588296475972910964312" ]
[ "nonn" ]
20
0
2
[ "A361768", "A361769" ]
null
Paul D. Hanna, Apr 06 2023
2023-04-07T22:40:39
oeisdata/seq/A361/A361769.seq
626f9e97151554b3087a98679c1e0611
A361770
Expansion of g.f. A(x) satisfying A(x) = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x)^2 + x^(n-1))^(n+1).
[ "1", "3", "14", "80", "510", "3498", "25145", "186972", "1426159", "11096944", "87736474", "702837098", "5692337206", "46533458472", "383450469145", "3181746494524", "26562082580277", "222941953595054", "1880174585677589", "15924467403391355", "135396623401761765", "1155230973031795808", "9888061401816818319" ]
[ "nonn" ]
15
0
2
[ "A359670", "A359711", "A361770", "A363135", "A363136", "A363137" ]
null
Paul D. Hanna, May 24 2023
2023-05-26T16:48:52
oeisdata/seq/A361/A361770.seq
44a3770ef8254f7ddea97815c198ce66
A361771
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(n-1).
[ "1", "1", "1", "7", "28", "89", "421", "1898", "7912", "36412", "169960", "779139", "3668210", "17486938", "83333003", "400956919", "1943928504", "9455346485", "46225027071", "227066384875", "1119123274755", "5534782142253", "27463607765186", "136652474592260", "681728348606011", "3409395265172439", "17088672210734316" ]
[ "nonn", "changed" ]
9
0
4
[ "A355865", "A357227", "A357232", "A359712", "A361771", "A361772", "A361773", "A361774" ]
null
Paul D. Hanna, May 13 2023
2025-04-22T21:55:57
oeisdata/seq/A361/A361771.seq
9721eec042bcdb8def5ba120c1fe3f7d
A361772
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(2*n-1).
[ "1", "1", "8", "61", "600", "6072", "65804", "733435", "8415694", "98529785", "1173278329", "14162417506", "172914841649", "2131621288494", "26495818020038", "331706510158239", "4178800564364333", "52935845003315662", "673878770026778330", "8616336680850069832", "110606714769468383785", "1424933340070339610543" ]
[ "nonn", "changed" ]
11
0
3
[ "A355865", "A357227", "A357232", "A359712", "A361771", "A361772", "A361773", "A361774", "A363112" ]
null
Paul D. Hanna, May 13 2023
2025-04-22T21:56:01
oeisdata/seq/A361/A361772.seq
31e1652883e579c7a9ff0f62f48b5b11
A361773
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(3*n-1).
[ "1", "2", "34", "677", "15660", "393790", "10433402", "286990626", "8117763488", "234635708480", "6899771599141", "205768408153474", "6208628685564955", "189188990142419693", "5813805339043713267", "179968235623379467274", "5606627898452185950618", "175650401043239524832783", "5530500462355496324862920" ]
[ "nonn", "changed" ]
11
0
2
[ "A355865", "A357227", "A357232", "A359712", "A361771", "A361772", "A361773", "A361774", "A363113" ]
null
Paul D. Hanna, May 13 2023
2025-04-22T21:55:52
oeisdata/seq/A361/A361773.seq
ce83e42d0f502249e2310e206bad8c63
A361774
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(4*n-1).
[ "1", "4", "150", "7003", "380817", "22517717", "1405927141", "91215539609", "6089092570148", "415519886498886", "28855638743197866", "2032628861705203315", "144884697917577076857", "10430845410431559928714", "757390467820895322043476", "55401570124877193188443429", "4078685155312165112343519832" ]
[ "nonn" ]
7
0
2
[ "A355865", "A357227", "A357232", "A359712", "A361771", "A361772", "A361773", "A361774", "A363114" ]
null
Paul D. Hanna, May 13 2023
2023-05-15T08:34:56
oeisdata/seq/A361/A361774.seq
c860eb367abdb39db71f6be129b8639d
A361775
Expansion of g.f. A(x) satisfying x = Sum_{n=-oo..+oo} (-1)^n * x^n * A(x)^n * (A(x)^n + x^n)^n.
[ "1", "1", "5", "21", "95", "405", "1680", "6926", "28257", "115254", "471785", "1908622", "7444553", "27617809", "101165030", "411727344", "1980777419", "9377434309", "30465401498", "5465053256", "-319249451709", "3800908753389", "79369582680985", "507720631888326", "-779604798853789", "-39876367011094054" ]
[ "sign" ]
13
0
3
[ "A292088", "A361775", "A361776" ]
null
Paul D. Hanna, May 08 2023
2023-08-05T14:29:23
oeisdata/seq/A361/A361775.seq
f560a5e418930738c0fd9cf32288dcba
A361776
Expansion of g.f. A(x) satisfying x*A(x) = Sum_{n=-oo..+oo} (-1)^n * x^n * A(x)^n * (A(x)^n + x^n)^n.
[ "1", "1", "6", "33", "198", "1204", "7522", "48270", "316281", "2110018", "14293494", "98054885", "679735489", "4753912524", "33504984427", "237767467381", "1697719206178", "12188097989345", "87913304459342", "636736565338008", "4628839922257617", "33767007201285762", "247145222148251103", "1814452818239003585" ]
[ "sign" ]
10
0
3
[ "A361775", "A361776" ]
null
Paul D. Hanna, May 08 2023
2023-05-10T09:42:18
oeisdata/seq/A361/A361776.seq
860125d1fa29e857547f476af52a9f4a
A361777
Expansion of e.g.f. A(x) satisfying A(x) = exp( x * A(x)^x ).
[ "1", "1", "1", "7", "25", "241", "1561", "19951", "188497", "3032065", "37720081", "734331511", "11341504681", "259658249137", "4792613587945", "126280535523871", "2712093428032801", "80881163134899841", "1981706113050012577", "66009436508505875815", "1817280748378601067961", "66887742743997848317681" ]
[ "nonn" ]
32
0
4
[ "A000272", "A361777" ]
null
Paul D. Hanna, Apr 17 2023
2023-05-03T04:37:51
oeisdata/seq/A361/A361777.seq
3abdaa99fe1c17118d29d751492dcee9
A361778
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * ((-x)^(n-1) - 2*A(x))^n.
[ "1", "2", "7", "27", "109", "459", "2006", "9017", "41384", "193048", "912571", "4361939", "21045710", "102361864", "501349447", "2470556294", "12240270901", "60935582862", "304660949343", "1529125824203", "7701783889261", "38915600049447", "197206343307012", "1002023916642621", "5103911800972155", "26056404563941575" ]
[ "nonn" ]
27
0
2
[ "A355865", "A357227", "A359712", "A361778" ]
null
Paul D. Hanna, May 10 2023
2023-05-12T06:35:54
oeisdata/seq/A361/A361778.seq
e9c57c1fdd9a46b30ccbf49bd24c3b9f
A361779
Expansion of g.f. A(x) satisfying 1/x = Sum_{n=-oo..+oo} x^n * (x^(2*n) - (-1)^n*A(x))^(n+1).
[ "1", "1", "2", "5", "10", "21", "51", "121", "282", "688", "1704", "4212", "10528", "26626", "67630", "172590", "443156", "1143034", "2958829", "7687875", "20043717", "52410511", "137417383", "361225349", "951755240", "2513057208", "6648904064", "17624116631", "46796906873", "124460500129", "331517863145", "884305712723", "2362007410465" ]
[ "nonn" ]
27
0
3
[ "A361778", "A361779" ]
null
Paul D. Hanna, May 10 2023
2023-05-11T14:23:25
oeisdata/seq/A361/A361779.seq
58cbce7752518b621c9f12f8a581fd6d
A361780
Numbers that have digits consisting only of line segments {1, 4, 7} or curved digits {0, 3, 6, 8, 9}.
[ "0", "1", "3", "4", "6", "7", "8", "9", "10", "11", "13", "14", "16", "17", "18", "19", "30", "31", "33", "34", "36", "37", "38", "39", "40", "41", "43", "44", "46", "47", "48", "49", "60", "61", "63", "64", "66", "67", "68", "69", "70", "71", "73", "74", "76", "77", "78", "79", "80", "81", "83", "84", "86", "87", "88", "89", "90", "91", "93", "94", "96", "97", "98", "99", "100", "101", "103", "104", "106", "107", "108", "109", "110" ]
[ "nonn", "base", "less" ]
17
1
3
[ "A028373", "A028374", "A072960", "A072961", "A082741", "A361780" ]
null
Bernard Schott, Mar 23 2023
2023-03-24T17:41:21
oeisdata/seq/A361/A361780.seq
7e2e75ac3aeed8b8eaa15effbdedb242
A361781
A(n,k) is the n-th term of the k-th inverse binomial transform of the Bell numbers (A000110); square array A(n,k), n>=0, k>=0, read by antidiagonals.
[ "1", "1", "1", "1", "0", "2", "1", "-1", "1", "5", "1", "-2", "2", "1", "15", "1", "-3", "5", "-3", "4", "52", "1", "-4", "10", "-13", "7", "11", "203", "1", "-5", "17", "-35", "36", "-10", "41", "877", "1", "-6", "26", "-75", "127", "-101", "31", "162", "4140", "1", "-7", "37", "-139", "340", "-472", "293", "-21", "715", "21147", "1", "-8", "50", "-233", "759", "-1573", "1787", "-848", "204", "3425", "115975" ]
[ "sign", "tabl" ]
28
0
6
[ "A000012", "A000110", "A000296", "A024000", "A108087", "A126617", "A160457", "A290219", "A346738", "A346739", "A346740", "A361380", "A361781" ]
null
Alois P. Heinz, Mar 23 2023
2024-06-13T01:48:57
oeisdata/seq/A361/A361781.seq
d591bf6565e5d2ebd9602780ceb9f25c
A361782
Numerators of the harmonic means of the bi-unitary divisors of the positive integers.
[ "1", "4", "3", "8", "5", "2", "7", "32", "9", "20", "11", "12", "13", "7", "5", "64", "17", "12", "19", "8", "21", "22", "23", "16", "25", "52", "27", "14", "29", "10", "31", "64", "11", "68", "35", "72", "37", "38", "39", "32", "41", "7", "43", "44", "3", "23", "47", "32", "49", "100", "17", "104", "53", "18", "55", "56", "57", "116", "59", "4", "61", "31", "63", "384", "65", "11", "67", "136" ]
[ "nonn", "frac" ]
10
1
2
[ "A099377", "A103339", "A188999", "A222266", "A286324", "A361316", "A361782", "A361783" ]
null
Amiram Eldar, Mar 24 2023
2023-03-24T09:33:29
oeisdata/seq/A361/A361782.seq
e77bd66a35a46297fcf26b8df677baad
A361783
Denominators of the harmonic means of the bi-unitary divisors of the positive integers.
[ "1", "3", "2", "5", "3", "1", "4", "15", "5", "9", "6", "5", "7", "3", "2", "27", "9", "5", "10", "3", "8", "9", "12", "5", "13", "21", "10", "5", "15", "3", "16", "21", "4", "27", "12", "25", "19", "15", "14", "9", "21", "2", "22", "15", "1", "9", "24", "9", "25", "39", "6", "35", "27", "5", "18", "15", "20", "45", "30", "1", "31", "12", "20", "119", "21", "3", "34", "45", "8", "9", "36", "25", "37", "57" ]
[ "nonn", "frac" ]
9
1
2
[ "A099378", "A103340", "A188999", "A222266", "A286324", "A286325", "A361317", "A361782", "A361783" ]
null
Amiram Eldar, Mar 24 2023
2023-03-24T11:15:04
oeisdata/seq/A361/A361783.seq
c800e5d563f9b02ec88a51c0c6c588e7
A361784
Harmonic means the bi-unitary divisors of the bi-unitary harmonic numbers (A286325).
[ "1", "2", "3", "4", "4", "6", "7", "7", "8", "11", "13", "13", "12", "10", "16", "7", "18", "16", "15", "24", "15", "20", "20", "18", "14", "22", "25", "24", "19", "25", "23", "27", "33", "31", "44", "32", "34", "30", "25", "36", "13", "46", "31", "21", "29", "40", "38", "33", "28", "40", "48", "38", "29", "45", "34", "47", "28", "32", "32", "44", "60", "27", "32", "28", "46", "26", "51" ]
[ "nonn" ]
9
1
2
[ "A001600", "A006087", "A188999", "A286324", "A286325", "A361318", "A361782", "A361783", "A361784" ]
null
Amiram Eldar, Mar 24 2023
2023-03-24T11:15:14
oeisdata/seq/A361/A361784.seq
63aecf99b271bf74381f6efd9475e198
A361785
Indices of records in the sequence of bi-unitary harmonic means A361782(k)/A361783(k).
[ "1", "2", "3", "4", "5", "6", "8", "10", "12", "15", "20", "24", "30", "40", "54", "56", "60", "84", "96", "120", "168", "210", "240", "270", "280", "360", "420", "480", "672", "840", "1080", "1320", "1512", "1680", "1890", "2160", "2310", "2520", "3080", "3360", "4320", "5280", "6048", "7392", "7560", "9240", "10920", "11880", "14040", "15120", "18480", "20790" ]
[ "nonn" ]
10
1
2
[ "A179971", "A292983", "A292984", "A293185", "A348654", "A361319", "A361782", "A361783", "A361785" ]
null
Amiram Eldar, Mar 24 2023
2023-03-24T11:14:36
oeisdata/seq/A361/A361785.seq
e027a660fd3e1729770fac71a71b5e8f
A361786
Bi-unitary arithmetic numbers: numbers for which the arithmetic mean of the bi-unitary divisors is an integer.
[ "1", "3", "5", "6", "7", "9", "11", "12", "13", "14", "15", "17", "19", "21", "22", "23", "25", "27", "28", "29", "30", "31", "33", "35", "37", "38", "39", "41", "42", "43", "44", "45", "46", "47", "49", "51", "53", "54", "55", "56", "57", "59", "60", "61", "62", "63", "65", "66", "67", "69", "70", "71", "73", "75", "76", "77", "78", "79", "81", "83", "84", "85", "86", "87", "89", "91", "92", "93", "94", "95", "96", "97", "99" ]
[ "nonn" ]
9
1
2
[ "A003601", "A103826", "A188999", "A222266", "A286324", "A361386", "A361786" ]
null
Amiram Eldar, Mar 24 2023
2023-03-24T11:12:55
oeisdata/seq/A361/A361786.seq
82cdb142fa3153789a0aa2739c9c5e3f
A361787
Bi-unitary arithmetic numbers k whose mean bi-unitary divisor is a bi-unitary divisor of k.
[ "1", "6", "60", "270", "420", "630", "672", "2970", "5460", "8190", "10080", "22848", "30240", "99792", "136500", "172900", "204750", "208656", "245700", "249480", "312480", "332640", "342720", "385560", "491400", "695520", "708288", "791700", "819000", "861840", "1028160", "1037400", "1187550", "1228500", "1421280", "1528800", "1571328" ]
[ "nonn" ]
9
1
2
[ "A007340", "A188999", "A222266", "A286324", "A286325", "A353039", "A361387", "A361786", "A361787" ]
null
Amiram Eldar, Mar 24 2023
2023-03-24T11:39:06
oeisdata/seq/A361/A361787.seq
c0207c5744af2420527170b2e6fc395a
A361788
Number of divisors of n that are totient values (A002202).
[ "1", "2", "1", "3", "1", "3", "1", "4", "1", "3", "1", "5", "1", "2", "1", "5", "1", "4", "1", "5", "1", "3", "1", "7", "1", "2", "1", "4", "1", "5", "1", "6", "1", "2", "1", "7", "1", "2", "1", "7", "1", "4", "1", "5", "1", "3", "1", "9", "1", "3", "1", "4", "1", "5", "1", "6", "1", "3", "1", "9", "1", "2", "1", "7", "1", "5", "1", "3", "1", "4", "1", "10", "1", "2", "1", "3", "1", "4", "1", "9", "1", "3", "1", "8", "1", "2", "1", "7", "1", "6" ]
[ "nonn" ]
6
1
2
[ "A000005", "A000079", "A005408", "A361788" ]
null
Michel Marcus, Mar 24 2023
2023-03-24T09:04:53
oeisdata/seq/A361/A361788.seq
50d77f7e81d2b4dd02e9f4271ee576d7
A361789
A(n, k) is the sum of the distinct terms in the dual Zeckendorf representations of n or of k; square array A(n, k) read by antidiagonals, n, k >= 0.
[ "0", "1", "1", "2", "1", "2", "3", "3", "3", "3", "4", "3", "2", "3", "4", "5", "4", "3", "3", "4", "5", "6", "6", "6", "3", "6", "6", "6", "7", "6", "5", "6", "6", "5", "6", "7", "8", "8", "6", "6", "4", "6", "6", "8", "8", "9", "8", "7", "6", "6", "6", "6", "7", "8", "9", "10", "9", "8", "8", "6", "5", "6", "8", "8", "9", "10", "11", "11", "11", "8", "11", "6", "6", "11", "8", "11", "11", "11", "12", "11", "10", "11", "11", "10", "6", "10", "11", "11", "10", "11", "12" ]
[ "nonn", "base", "tabl" ]
8
0
4
[ "A003754", "A003986", "A022290", "A334348", "A356771", "A356969", "A361756", "A361789" ]
null
Rémy Sigrist, Mar 24 2023
2023-03-26T10:30:00
oeisdata/seq/A361/A361789.seq
3c50fdd9e6787d1a62a3b3af3bae2c14
A361790
Expansion of 1/sqrt(1 - 4*x/(1+x)^4).
[ "1", "2", "-2", "-8", "6", "42", "-8", "-228", "-90", "1210", "1238", "-6116", "-10864", "28574", "80932", "-116248", "-548010", "339678", "3455686", "173208", "-20452674", "-14036418", "113365140", "156407916", "-580805472", "-1312098918", "2659610562", "9621079540", "-9902139124", "-64566648122", "18521111032" ]
[ "sign" ]
20
0
2
[ "A006139", "A137635", "A360133", "A361790", "A361791", "A361792" ]
null
Seiichi Manyama, Mar 24 2023
2024-07-11T14:43:46
oeisdata/seq/A361/A361790.seq
cf4d3661f1c18bce14d2993cba01d953
A361791
Expansion of 1/sqrt(1 - 4*x/(1+x)^5).
[ "1", "2", "-4", "-10", "30", "72", "-238", "-580", "1970", "4910", "-16734", "-42750", "144600", "379000", "-1264700", "-3402480", "11160730", "30828070", "-99168820", "-281279030", "885931600", "2580541580", "-7948885910", "-23779051760", "71572652480", "219906488302", "-646332447086", "-2039738985238", "5850898295170" ]
[ "sign" ]
22
0
2
[ "A006139", "A137635", "A359758", "A360133", "A361790", "A361791", "A361792" ]
null
Seiichi Manyama, Mar 24 2023
2024-07-12T16:39:52
oeisdata/seq/A361/A361791.seq
54770af9fac1e5eee13d919a4c271abe
A361792
Expansion of 1/sqrt(1 - 4*x/(1+x)^6).
[ "1", "2", "-6", "-10", "66", "60", "-750", "-236", "8682", "-2098", "-100792", "80286", "1162458", "-1603412", "-13225764", "26767020", "147428498", "-409582818", "-1596563202", "5941802122", "16587101544", "-83014131140", "-161717252990", "1126247965980", "1411774064970", "-14905602076350" ]
[ "sign" ]
23
0
2
[ "A006139", "A137635", "A360132", "A360133", "A361790", "A361791", "A361792" ]
null
Seiichi Manyama, Mar 24 2023
2024-07-12T16:40:53
oeisdata/seq/A361/A361792.seq
1fdd55a4270efe0e13d29cfdf85b6710
A361793
Sum of the squares d^2 of the divisors d satisfying d^3|n.
[ "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "10", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "10", "1", "5", "1", "1", "1", "1", "1", "1", "1", "21", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "1", "1", "5" ]
[ "nonn", "mult", "easy" ]
30
1
8
[ "A035316", "A069290", "A333843", "A361793" ]
null
R. J. Mathar, Mar 24 2023
2024-06-26T04:32:50
oeisdata/seq/A361/A361793.seq
b906d4a8b58cbc28d0c747da98f7561f
A361794
Sum of the cubes d^3 of the divisors d satisfying d^2|n.
[ "1", "1", "1", "9", "1", "1", "1", "9", "28", "1", "1", "9", "1", "1", "1", "73", "1", "28", "1", "9", "1", "1", "1", "9", "126", "1", "28", "9", "1", "1", "1", "73", "1", "1", "1", "252", "1", "1", "1", "9", "1", "1", "1", "9", "28", "1", "1", "73", "344", "126", "1", "9", "1", "28", "1", "9", "1", "1", "1", "9", "1", "1", "28", "585", "1", "1", "1", "9", "1", "1", "1", "252", "1", "1", "126", "9", "1", "1", "1", "73" ]
[ "nonn", "mult", "easy" ]
30
1
4
[ "A010052", "A035316", "A069290", "A333843", "A333844", "A351308", "A361794" ]
null
R. J. Mathar, Mar 24 2023
2024-06-10T15:01:09
oeisdata/seq/A361/A361794.seq
1ab02876d3af5e28a7a59bdd1f4278e4
A361795
a(n) is the area of the largest rectangle with integer sides that can be drawn inside a circle of diameter n.
[ "0", "0", "1", "4", "6", "12", "16", "20", "30", "36", "49", "56", "64", "81", "90", "110", "121", "144", "156", "169", "196", "210", "240", "256", "272", "306", "324", "361", "380", "420", "441", "462", "506", "529", "576", "600", "625", "676", "702", "756", "784", "812", "870", "900", "961", "992", "1056", "1089", "1122", "1190" ]
[ "nonn" ]
8
0
4
[ "A049472", "A049473", "A361795" ]
null
John Mason, Mar 24 2023
2023-03-24T17:36:16
oeisdata/seq/A361/A361795.seq
c473bd4d9136fa3c4bd763b266639675
A361796
Prime numbers preceded by two consecutive numbers which are products of four distinct primes (or tetraprimes).
[ "8647", "15107", "20407", "20771", "21491", "23003", "23531", "24767", "24971", "27967", "29147", "33287", "34847", "36779", "42187", "42407", "42667", "43331", "43991", "46807", "46867", "51431", "52691", "52747", "53891", "54167", "58567", "63247", "63367", "69379", "71711", "73607", "73867", "74167", "76507", "76631", "76847", "80447", "83591", "84247", "86243" ]
[ "nonn" ]
51
1
1
[ "A000040", "A046386", "A140078", "A361796", "A362578" ]
null
Massimo Kofler, Apr 26 2023
2025-01-29T19:28:50
oeisdata/seq/A361/A361796.seq
5a4cd50ce567996049cc19fb9709921c
A361797
Even numbers k which have fewer divisors than both neighboring odd numbers, i.e., tau(k) < min{tau(k-1), tau(k+1)}.
[ "274", "386", "626", "926", "1126", "1174", "1234", "1546", "1574", "1594", "1646", "1774", "1814", "1954", "2036", "2066", "2092", "2186", "2234", "2276", "2302", "2374", "2386", "2402", "2404", "2554", "2638", "2738", "2876", "2906", "3158", "3244", "3334", "3394", "3446", "3554", "3566", "3574", "3758", "3814", "3994", "4124", "4166", "4174" ]
[ "nonn" ]
44
1
1
[ "A000005", "A075025", "A361797" ]
null
Steven Lu, Mar 25 2023
2025-01-29T19:29:13
oeisdata/seq/A361/A361797.seq
5bc3008f7a6beeb70c4360f03a43e279
A361798
Distinct sums of contiguous subsequences in A362040.
[ "0", "1", "2", "3", "4", "6", "7", "10", "11", "13", "14", "15", "17", "21", "23", "24", "25", "26", "32", "34", "36", "38", "39", "42", "46", "47", "52", "53", "57", "59", "60", "62", "63", "72", "75", "76", "79", "81", "83", "85", "86", "94", "96", "102", "106", "109", "113", "115", "117", "119", "120", "123", "125", "128", "138", "142", "148", "154", "155", "157", "159", "160", "161", "162", "175", "179", "182", "190", "191", "197", "200", "205", "207", "211", "213", "214" ]
[ "nonn" ]
27
1
3
[ "A361798", "A362040" ]
null
Neal Gersh Tolunsky, Apr 16 2023
2023-09-14T09:16:34
oeisdata/seq/A361/A361798.seq
ef768454b8d19426aa044c57928808d3
A361799
Numbers which cannot be expressed as i^2 + j*k with i >= j >= k >= 0.
[ "3", "7", "14", "21", "23", "43", "47", "62", "75", "119", "134", "138", "167", "215", "318", "398", "566", "1487" ]
[ "nonn", "more" ]
20
1
1
null
null
Gordon Hamilton, Mar 24 2023
2024-05-04T02:47:44
oeisdata/seq/A361/A361799.seq
22b028e70e38921ceaf618fbebb3a417
A361800
Number of integer partitions of n with the same length as median.
[ "1", "0", "0", "2", "0", "0", "1", "2", "3", "3", "3", "3", "4", "6", "9", "13", "14", "15", "18", "21", "27", "32", "40", "46", "55", "62", "72", "82", "95", "111", "131", "157", "186", "225", "264", "316", "366", "430", "495", "578", "663", "768", "880", "1011", "1151", "1316", "1489", "1690", "1910", "2158", "2432", "2751", "3100", "3505", "3964", "4486", "5079", "5764" ]
[ "nonn" ]
15
1
4
[ "A000009", "A000041", "A000975", "A006141", "A008284", "A013580", "A027193", "A047993", "A053263", "A079309", "A206240", "A237753", "A237757", "A240219", "A307683", "A325347", "A359893", "A359901", "A360005", "A361800", "A361849", "A361860", "A362048", "A362049", "A362050" ]
null
Gus Wiseman, Apr 07 2023
2023-04-22T09:28:05
oeisdata/seq/A361/A361800.seq
81680b70d6ca9b879edd9b57e2742aaa