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666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A356001
Expansion of e.g.f. -LambertW((1 - exp(3*x))/3).
[ "0", "1", "5", "36", "379", "5461", "100476", "2250613", "59432141", "1807959042", "62262816157", "2394551966401", "101724440338494", "4730814590128615", "239057921691911861", "13042779411190737420", "764136645388807739239", "47846833035272035228849", "3188740106752561252031364" ]
[ "nonn" ]
23
0
3
[ "A048802", "A356000", "A356001", "A357336" ]
null
Seiichi Manyama, Sep 24 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356001.seq
eb4cbbdc0f3dc5c878194b9ff0e39914
A356002
A family of triangles T(m), m >= 0, read by triangles and then by rows; triangle T(0) is [1; 1, 1]; for m >= 0, triangle T(m+1) is obtained by replacing each subtriangle [t; u, v] in T(m) by [t; 2*t+u, 2*t+v; t+2*u, t+u+v, t+2*v; u, 2*u+v, u+2*v, v].
[ "1", "1", "1", "1", "3", "3", "3", "3", "3", "1", "3", "3", "1", "1", "5", "5", "7", "7", "7", "3", "9", "9", "3", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "3", "9", "9", "3", "9", "9", "3", "7", "9", "9", "9", "9", "9", "9", "7", "5", "7", "9", "9", "9", "9", "9", "7", "5", "1", "5", "7", "3", "9", "9", "3", "7", "5", "1", "1", "7", "7", "11", "11", "11", "5", "15", "15", "5", "17", "17", "17", "17", "17" ]
[ "nonn", "tabf" ]
16
0
5
[ "A177407", "A355855", "A356002" ]
null
Rémy Sigrist, Jul 22 2022
2023-01-18T03:28:54
oeisdata/seq/A356/A356002.seq
3434459f9812291763cc2569d7d98bf4
A356003
Primes p such that p = 3*a + 1 with p + a*a*(a+1) prime or p = 3*a + 2 with p + a*(a+1)*(a+1) prime.
[ "2", "7", "11", "17", "19", "29", "61", "89", "97", "127", "179", "251", "263", "269", "277", "307", "331", "397", "433", "439", "457", "467", "479", "523", "569", "601", "647", "739", "773", "809", "863", "883", "937", "953", "971", "1063", "1087", "1091", "1171", "1181", "1307", "1447", "1483", "1511", "1583", "1621", "1657", "1663", "1783", "1789", "1801", "1811", "1879", "1889", "1933", "1951", "1987" ]
[ "nonn" ]
10
1
1
null
null
J. M. Bergot and Robert Israel, Jul 22 2022
2022-08-03T12:40:28
oeisdata/seq/A356/A356003.seq
10a1bebec932cf4a96ee355608de127e
A356004
a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d! * (k/d)!).
[ "1", "4", "14", "64", "322", "2054", "14380", "116722", "1060580", "10636042", "116996464", "1411275650", "18346583452", "256869465610", "3856674412952", "61743633813634", "1049641774831780", "18896533652098442", "359034139389870400", "7182372973523436802", "150833211474559084844" ]
[ "nonn" ]
11
1
2
[ "A002627", "A121860", "A355886", "A355991", "A356004" ]
null
Seiichi Manyama, Jul 22 2022
2022-07-22T16:44:08
oeisdata/seq/A356/A356004.seq
d31b167a2426b36180e7460cd9ec0aed
A356005
Number of integers k such that k*tau(k) <= n.
[ "1", "1", "1", "2", "2", "3", "3", "3", "3", "4", "4", "5", "5", "6", "6", "6", "6", "6", "6", "6", "6", "7", "7", "8", "8", "9", "10", "10", "10", "10", "10", "11", "11", "12", "12", "12", "12", "13", "13", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "16", "16", "17", "17", "18", "18", "19", "19", "19", "19", "19", "19", "19", "19", "19", "19", "20", "20", "21", "22", "22", "22", "22", "22" ]
[ "nonn" ]
20
1
4
[ "A038040", "A327166", "A356005" ]
null
Benoit Cloitre, Jul 22 2022
2022-07-23T09:58:15
oeisdata/seq/A356/A356005.seq
34bed4f20b768bfec273ae4e9f9a479e
A356006
The number of prime divisors of n that are not greater than 5, counted with multiplicity.
[ "0", "1", "1", "2", "1", "2", "0", "3", "2", "2", "0", "3", "0", "1", "2", "4", "0", "3", "0", "3", "1", "1", "0", "4", "2", "1", "3", "2", "0", "3", "0", "5", "1", "1", "1", "4", "0", "1", "1", "4", "0", "2", "0", "2", "3", "1", "0", "5", "0", "3", "1", "2", "0", "4", "1", "3", "1", "1", "0", "4", "0", "1", "2", "6", "1", "2", "0", "2", "1", "2", "0", "5", "0", "1", "3", "2", "0", "2", "0", "5", "4", "1", "0", "3", "1", "1", "1" ]
[ "nonn", "easy" ]
20
1
4
[ "A001222", "A007814", "A007949", "A112759", "A112765", "A169611", "A355582", "A355583", "A355584", "A356006" ]
null
Amiram Eldar, Jul 23 2022
2022-07-26T10:10:08
oeisdata/seq/A356/A356006.seq
884f8714ffe83eff7e6e1c596792440c
A356007
Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive terms contains only one pair whose numbers of divisors are not coprime.
[ "1", "2", "3", "4", "5", "6", "9", "10", "11", "16", "17", "18", "64", "65", "66", "81", "82", "83", "100", "101", "102", "121", "122", "123", "144", "145", "146", "169", "170", "173", "196", "197", "199", "225", "226", "227", "256", "257", "258", "289", "290", "291", "324", "326", "327", "361", "362", "365", "400", "401", "402", "441", "442", "443", "484", "485", "487", "529", "530", "533", "576", "577", "579" ]
[ "nonn" ]
4
1
2
[ "A353187", "A356007" ]
null
Ivan N. Ianakiev, Jul 23 2022
2022-08-24T09:53:24
oeisdata/seq/A356/A356007.seq
018b1b3a8d0fbfebca6417cdf975c26d
A356008
A variant of Look and Say sequence (A005150) based on exponents in prime factorization of n (see Comments section for precise definition).
[ "1", "6", "105", "12", "315", "18", "945", "24", "525", "6006", "2835", "420", "8505", "42042", "735", "48", "25515", "1050", "76545", "12012", "440895", "294294", "229635", "840", "1575", "2060058", "2625", "84084", "688905", "54", "2066715", "96", "5731635", "14420406", "2205", "36", "6200145", "100942842", "74511255", "24024", "18600435" ]
[ "nonn" ]
7
1
2
[ "A002110", "A005150", "A007814", "A008776", "A067255", "A244990", "A356008", "A356014", "A356016" ]
null
Rémy Sigrist, Jul 23 2022
2022-07-25T10:43:34
oeisdata/seq/A356/A356008.seq
87dad395ca6b78f8a476af2c8502f0ca
A356009
a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)!).
[ "1", "4", "15", "73", "390", "2641", "19208", "164585", "1541746", "16158341", "181370552", "2283224065", "30160914446", "434715492485", "6655132252876", "109315669969217", "1879289179364690", "34719396682318021", "666070910669770400", "13590051478686198401", "289043813095242038422" ]
[ "nonn" ]
8
1
2
[ "A087906", "A356004", "A356009" ]
null
Seiichi Manyama, Jul 23 2022
2022-07-23T09:53:57
oeisdata/seq/A356/A356009.seq
95e44c908c090ba5703fe50af4be63d5
A356010
a(n) = n! * Sum_{k=1..n} floor(n/k)/k.
[ "1", "5", "23", "134", "814", "6324", "50028", "475824", "4806576", "54597600", "644119200", "8847100800", "121718332800", "1853505158400", "29894856364800", "518855607244800", "9197155541145600", "179420609436364800", "3537039053405491200", "75849875285280768000", "1670700245252548608000" ]
[ "nonn" ]
16
1
2
[ "A038048", "A355886", "A356010" ]
null
Seiichi Manyama, Jul 23 2022
2022-08-07T04:57:27
oeisdata/seq/A356/A356010.seq
99a06f7665af04679d4353709160ef93
A356011
a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)).
[ "1", "2", "6", "17", "80", "337", "2240", "14681", "117010", "1023941", "10900472", "108881665", "1375544846", "17732140805", "247041590476", "3605768497217", "59990390084690", "977383707751621", "18214603019184800", "337615168055209601", "6763842079452393622", "141262515443311046885" ]
[ "nonn" ]
12
1
2
[ "A345682", "A345683", "A355991", "A356011", "A356013", "A356015" ]
null
Seiichi Manyama, Jul 23 2022
2022-07-23T09:54:04
oeisdata/seq/A356/A356011.seq
81cbe26f06cefb76cb21e175c4e65c3a
A356012
a(n) = n! / (6 * floor(n/3)).
[ "1", "4", "20", "60", "420", "3360", "20160", "201600", "2217600", "19958400", "259459200", "3632428800", "43589145600", "697426329600", "11856247603200", "177843714048000", "3379030566912000", "67580611338240000", "1216451004088320000", "26761922089943040000", "615524208068689920000" ]
[ "nonn", "easy" ]
11
3
2
[ "A355990", "A356012", "A356013" ]
null
Seiichi Manyama, Jul 23 2022
2024-07-25T14:45:36
oeisdata/seq/A356/A356012.seq
28f703801ff20f8e15fd70862a46e822
A356013
Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)).
[ "1", "1", "1", "2", "3", "1", "6", "6", "4", "1", "24", "30", "20", "5", "1", "120", "120", "60", "30", "6", "1", "720", "840", "420", "210", "42", "7", "1", "5040", "5040", "3360", "840", "336", "56", "8", "1", "40320", "45360", "20160", "7560", "3024", "504", "72", "9", "1", "362880", "362880", "201600", "75600", "15120", "5040", "720", "90", "10", "1" ]
[ "nonn", "tabl" ]
12
1
4
[ "A000142", "A265376", "A355996", "A356011", "A356012", "A356013" ]
null
Seiichi Manyama, Jul 23 2022
2022-07-23T09:54:12
oeisdata/seq/A356/A356013.seq
226434263a6ad2d632e7c8b6cde9b4d1
A356014
Consider the exponents in the prime factorization of n, and replace each run of k consecutive e's by a unique e; the resulting list corresponds to the exponents in the prime factorization of a(n).
[ "1", "2", "3", "4", "3", "2", "3", "8", "9", "10", "3", "12", "3", "10", "3", "16", "3", "18", "3", "20", "21", "10", "3", "24", "9", "10", "27", "20", "3", "2", "3", "32", "21", "10", "3", "4", "3", "10", "21", "40", "3", "10", "3", "20", "45", "10", "3", "48", "9", "50", "21", "20", "3", "54", "21", "40", "21", "10", "3", "12", "3", "10", "63", "64", "21", "10", "3", "20", "21", "10", "3", "72", "3" ]
[ "nonn" ]
9
1
2
[ "A007814", "A061742", "A067255", "A090079", "A115964", "A294674", "A319521", "A337864", "A356008", "A356014", "A356021" ]
null
Rémy Sigrist, Jul 23 2022
2022-07-25T10:43:29
oeisdata/seq/A356/A356014.seq
9f33b0159b24375e8125ffba87600455
A356015
a(n) = n! * Sum_{k=1..n} 1/(k * floor(n/k)!).
[ "1", "2", "6", "21", "125", "625", "5089", "38185", "343657", "3376081", "40765681", "427649761", "6038448481", "84486386881", "1252766088001", "19388604009601", "350529058051201", "5938944734419201", "119242323659692801", "2303746722596390401", "48358406991122726401", "1063884813011759692801" ]
[ "nonn" ]
5
1
2
[ "A355987", "A356011", "A356015" ]
null
Seiichi Manyama, Jul 23 2022
2022-07-23T09:54:16
oeisdata/seq/A356/A356015.seq
b5fdf0125c25a00b1800452abb3abd95
A356016
Consider the exponents in the prime factorization of n, and replace each run of k consecutive e's by a unique k; the resulting list corresponds to the exponents in the prime factorization of a(n).
[ "1", "2", "6", "2", "12", "4", "24", "2", "6", "30", "48", "6", "96", "90", "18", "2", "192", "6", "384", "30", "210", "270", "768", "6", "12", "810", "6", "90", "1536", "8", "3072", "2", "1050", "2430", "36", "4", "6144", "7290", "5250", "30", "12288", "60", "24576", "270", "30", "21870", "49152", "6", "24", "30", "26250", "810", "98304", "6", "420", "90", "131250" ]
[ "nonn" ]
9
1
2
[ "A002110", "A067255", "A318928", "A319522", "A356008", "A356014", "A356016" ]
null
Rémy Sigrist, Jul 23 2022
2022-07-25T10:43:24
oeisdata/seq/A356/A356016.seq
cbd7e23fda45a0babd4a850df55ab1de
A356017
The fixed points of A355702.
[ "1", "2", "3", "12", "30", "54", "60", "92", "165", "186", "190", "247", "249", "287", "446", "671", "674", "910", "1089", "6310", "6335", "6815", "6844", "9116", "9243", "10215", "11805", "12234", "12244", "12249", "12467", "12522", "13074", "13481", "13556", "13564", "14751", "15505", "15597", "16158", "16220", "16232", "16242", "16306", "17036", "18069", "18578", "21742" ]
[ "nonn" ]
8
1
2
[ "A355702", "A356017" ]
null
Scott R. Shannon, Jul 23 2022
2022-07-24T02:30:04
oeisdata/seq/A356/A356017.seq
98ddbd21a3c36b04c75a41da67b907b2
A356018
a(n) is the number of evil divisors (A001969) of n.
[ "0", "0", "1", "0", "1", "2", "0", "0", "2", "2", "0", "3", "0", "0", "3", "0", "1", "4", "0", "3", "1", "0", "1", "4", "1", "0", "3", "0", "1", "6", "0", "0", "2", "2", "1", "6", "0", "0", "2", "4", "0", "2", "1", "0", "5", "2", "0", "5", "0", "2", "3", "0", "1", "6", "1", "0", "2", "2", "0", "9", "0", "0", "3", "0", "2", "4", "0", "3", "2", "2", "1", "8", "0", "0", "4", "0", "1", "4", "0", "5", "3", "0", "1", "3", "3", "2" ]
[ "nonn", "easy", "base" ]
28
1
6
[ "A000005", "A001969", "A083230", "A087990", "A087991", "A093688", "A093696", "A227872", "A332268", "A355302", "A356018", "A356019", "A356020" ]
null
Bernard Schott, Jul 23 2022
2022-08-07T08:39:19
oeisdata/seq/A356/A356018.seq
6f39152c31e13b454ec1c9321aac49ab
A356019
a(n) is the smallest number that has exactly n evil divisors (A001969).
[ "1", "3", "6", "12", "18", "45", "30", "135", "72", "60", "90", "765", "120", "1575", "270", "180", "600", "3465", "480", "13545", "360", "540", "1530", "10395", "1260", "720", "3150", "1980", "1080", "49725", "1440", "45045", "2520", "3060", "6930", "2160", "3780", "58905", "27090", "6300", "5040", "184275", "4320", "135135", "6120", "7920", "20790", "329175", "7560", "8640" ]
[ "nonn", "base" ]
28
0
2
[ "A001969", "A087997", "A093688", "A227872", "A327328", "A333456", "A355303", "A355699", "A355968", "A356018", "A356019", "A356020", "A356040" ]
null
Bernard Schott, Jul 23 2022
2022-08-26T07:37:32
oeisdata/seq/A356/A356019.seq
7ff05e74533999da02f2206fc8b714df
A356020
Positions of records in A356018, i.e., integers whose number of evil divisors sets a new record.
[ "1", "3", "6", "12", "18", "30", "60", "90", "120", "180", "360", "540", "720", "1080", "1440", "2160", "3780", "4320", "6120", "7560", "8640", "12240", "15120", "24480", "27720", "30240", "36720", "48960", "50400", "55440", "73440", "83160", "110880", "128520", "138600", "166320", "221760", "257040", "277200", "332640", "471240", "514080", "554400" ]
[ "nonn", "base" ]
24
1
2
[ "A001969", "A093036", "A093037", "A093688", "A093696", "A330815", "A350756", "A355969", "A356018", "A356019", "A356020" ]
null
Bernard Schott, Jul 24 2022
2022-07-26T17:47:48
oeisdata/seq/A356/A356020.seq
8de6d87f22d868158c42a2b14585ffb9
A356021
Positive numbers k such that, for any consecutive prime numbers p, q <= A006530(n), the p-adic and q-adic valuations of n are different.
[ "1", "2", "3", "4", "8", "9", "10", "12", "16", "18", "20", "21", "24", "27", "32", "40", "45", "48", "50", "54", "63", "64", "72", "75", "80", "81", "84", "90", "96", "100", "108", "110", "126", "128", "135", "144", "147", "160", "162", "168", "189", "192", "200", "220", "243", "250", "256", "270", "273", "288", "300", "320", "324", "336", "350", "360", "375", "378", "384" ]
[ "nonn" ]
4
1
2
[ "A006530", "A066205", "A066206", "A356014", "A356021" ]
null
Rémy Sigrist, Jul 23 2022
2022-07-25T10:43:19
oeisdata/seq/A356/A356021.seq
bfd8a77432f0e2b9a1b438949a74edc7
A356022
Decimal expansion of the infinite series Sum_{j>=0} 1/2^^j where ^^ indicates tetration.
[ "1", "8", "1", "2", "5", "1", "5", "2", "5", "8", "7", "8", "9", "0", "6", "2", "5", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "cons" ]
37
1
2
[ "A007404", "A014221", "A356022", "A356023" ]
null
Marco Ripà, Jul 23 2022
2025-03-23T03:20:45
oeisdata/seq/A356/A356022.seq
fbde7c6b95acba7af814d27bf642436f
A356023
Decimal expansion of Sum_{j>=1} 2^^j/2^^(j+1) where ^^ indicates tetration.
[ "7", "5", "0", "2", "4", "4", "1", "4", "0", "6", "2", "5", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "cons" ]
33
0
1
[ "A356022", "A356023" ]
null
Marco Ripà, Jul 23 2022
2023-12-10T09:27:28
oeisdata/seq/A356/A356023.seq
3023dba03f210b04a6f090a579a954d5
A356024
a(n) is the next higher integer than n whose spelling in US English comes lexicographically later.
[ "2", "200", "12", "6", "6", "10", "10", "9", "10", "12", "12", "20", "20", "16", "16", "20", "20", "19", "20", "21", "22", "200", "200", "26", "26", "200", "200", "29", "200", "31", "32", "200", "200", "36", "36", "200", "200", "39", "200", "41", "42", "60", "60", "46", "46", "60", "60", "49", "60", "51", "52", "60", "60", "56", "56", "60", "60", "59", "60", "61", "62", "200", "200" ]
[ "nonn", "word" ]
6
1
1
[ "A180301", "A356024" ]
null
Michael S. Branicky, Jul 23 2022
2022-07-24T13:04:43
oeisdata/seq/A356/A356024.seq
5aab90d63190d62b2406af3d1ef1f819
A356025
Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k!) )^(1/(1-x)).
[ "1", "1", "5", "28", "206", "1786", "18347", "212745", "2773927", "39901109", "628298992", "10725440221", "197349522471", "3888090474399", "81659016005387", "1820049574958950", "42895622543757084", "1065460090285463634", "27811791343693345811", "760920657403831436463" ]
[ "nonn" ]
58
0
3
[ "A209902", "A356009", "A356025", "A356336" ]
null
Seiichi Manyama, Aug 04 2022
2022-08-04T11:00:17
oeisdata/seq/A356/A356025.seq
bda9cfbc3cc84f1ea4d0269717576b0a
A356026
Main diagonal of right-and-left variant of Kimberling expulsion array, A007063.
[ "1", "3", "5", "7", "4", "12", "10", "17", "6", "22", "15", "19", "24", "33", "31", "18", "8", "44", "35", "9", "39", "55", "26", "42", "29", "20", "14", "32", "58", "78", "76", "52", "38", "68", "74", "59", "67", "101", "27", "47", "88", "75", "61", "109", "50", "124", "54", "113", "41", "102", "119", "84", "34", "40", "136", "105", "71", "92", "131", "108", "28", "171", "169" ]
[ "nonn" ]
23
1
2
[ "A007063", "A355323", "A356026" ]
null
Clark Kimberling, Jul 23 2022
2025-06-29T18:15:12
oeisdata/seq/A356/A356026.seq
f8de4b7e61813c1319fd35e84a7e200e
A356027
Duplicate of A101391.
[ "1", "0", "1", "0", "2", "1", "0", "2", "3", "1", "0", "4", "6", "4", "1", "0", "2", "9", "10", "5", "1", "0", "6", "15", "20", "15", "6", "1", "0", "4", "18", "34", "35", "21", "7", "1", "0", "6", "27", "56", "70", "56", "28", "8", "1" ]
[ "dead" ]
26
1
5
null
null
null
2025-05-06T16:23:00
oeisdata/seq/A356/A356027.seq
21577c346513afae2f186b3869ada05c
A356028
Irregular triangle {A(n, k)} read by rows, giving in row n the numbers 1, 2, ..., 2^n - 1 ordered according to increasing binary weights, and for like weights decreasing.
[ "1", "2", "1", "3", "4", "2", "1", "6", "5", "3", "7", "8", "4", "2", "1", "12", "10", "9", "6", "5", "3", "14", "13", "11", "7", "15", "16", "8", "4", "2", "1", "24", "20", "18", "17", "12", "10", "9", "6", "5", "3", "28", "26", "25", "22", "21", "19", "14", "13", "11", "7", "30", "29", "27", "23", "15", "31", "32", "16", "8", "4", "2", "1", "48", "40", "36", "34", "33", "24", "20", "18", "17", "12", "10", "9", "6", "5", "3", "56", "52", "50", "49", "44", "42", "41", "38", "37", "35", "28", "26", "25", "22", "21", "19", "14", "13", "11", "7", "60", "58", "57", "54", "53", "51", "46", "45", "43", "39", "30", "29", "27", "23", "15", "62", "61", "59", "55", "47", "31", "63" ]
[ "nonn", "tabf", "base", "look", "easy" ]
27
1
2
[ "A000225", "A006516", "A134346", "A171476", "A262881", "A294648", "A356028" ]
null
Wolfdieter Lang, Jul 27 2022
2023-12-20T07:41:21
oeisdata/seq/A356/A356028.seq
aa0ca6b0a556de518a40b4f40f9ab053
A356029
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * (n - 2*k)!).
[ "1", "1", "1", "4", "13", "61", "421", "2626", "27049", "245953", "3069721", "40222216", "576988501", "10058716669", "169773404893", "3596206855606", "73450508303761", "1775382487932001", "43993288886533489", "1183551336464017708", "34806599282992709341", "1043452963148195577181" ]
[ "nonn" ]
46
0
4
[ "A354436", "A354550", "A356029", "A356328", "A356608", "A356628", "A356632" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-19T09:19:17
oeisdata/seq/A356/A356029.seq
874b8efac844dac6bbfe9b214ff182e9
A356030
Decimal expansion of the real root of x^3 - x - 2.
[ "1", "5", "2", "1", "3", "7", "9", "7", "0", "6", "8", "0", "4", "5", "6", "7", "5", "6", "9", "6", "0", "4", "0", "8", "0", "8", "3", "2", "2", "5", "4", "4", "3", "8", "5", "1", "4", "4", "2", "8", "3", "8", "9", "8", "2", "8", "4", "2", "7", "9", "0", "3", "9", "0", "9", "0", "9", "0", "4", "9", "8", "0", "1", "5", "4", "2", "8", "1", "5", "6", "4", "0", "3", "4", "3", "0", "5", "8", "8", "2", "1", "6", "0", "4", "9", "1", "6", "3", "7", "9", "2", "6", "9", "6", "7", "3", "3", "8", "7", "7", "0", "5", "6", "7", "9" ]
[ "nonn", "cons", "easy" ]
16
1
2
[ "A289265", "A356030", "A356031" ]
null
Wolfdieter Lang, Aug 19 2022
2023-06-18T01:52:17
oeisdata/seq/A356/A356030.seq
f6ca119bbfced3d574b654f8cdd19a3d
A356031
Decimal expansion of the real root of 2*x^3 + x - 1.
[ "5", "8", "9", "7", "5", "4", "5", "1", "2", "3", "0", "1", "4", "5", "8", "3", "8", "4", "2", "7", "8", "8", "0", "1", "7", "4", "7", "0", "9", "6", "0", "7", "1", "3", "6", "2", "4", "5", "1", "4", "3", "5", "1", "7", "3", "2", "2", "8", "3", "6", "2", "0", "7", "2", "3", "8", "8", "0", "7", "9", "3", "4", "1", "2", "3", "5", "0", "4", "8", "0", "2", "4", "1", "5", "7", "7" ]
[ "nonn", "cons", "easy" ]
16
0
1
[ "A356030", "A356031" ]
null
Wolfdieter Lang, Aug 19 2022
2024-02-04T15:42:39
oeisdata/seq/A356/A356031.seq
e6c75b24cdeacdfb1327b1d659e30e4c
A356032
Decimal expansion of the positive real root of x^4 + x - 1.
[ "7", "2", "4", "4", "9", "1", "9", "5", "9", "0", "0", "0", "5", "1", "5", "6", "1", "1", "5", "8", "8", "3", "7", "2", "2", "8", "2", "1", "8", "7", "0", "3", "6", "5", "6", "5", "7", "8", "6", "4", "9", "4", "4", "8", "1", "3", "5", "0", "0", "1", "1", "0", "1", "7", "2", "7", "0", "3", "9", "8", "0", "2", "8", "4", "3", "7", "4", "5", "2", "9", "0", "6", "4", "7", "5", "1" ]
[ "nonn", "cons", "easy", "changed" ]
33
0
1
[ "A060007", "A072223", "A086106", "A202538", "A356032", "A376658" ]
null
Wolfdieter Lang, Aug 27 2022
2025-07-14T10:11:09
oeisdata/seq/A356/A356032.seq
10191c83632716e73fa13a6408dc70fd
A356033
Decimal expansion of (-1 + sqrt(13))/6 = A223139/3.
[ "4", "3", "4", "2", "5", "8", "5", "4", "5", "9", "1", "0", "6", "6", "4", "8", "8", "2", "1", "8", "6", "5", "3", "6", "8", "7", "7", "9", "1", "1", "7", "4", "9", "3", "2", "4", "3", "7", "5", "2", "1", "6", "0", "9", "5", "6", "4", "0", "8", "7", "4", "3", "6", "8", "7", "8", "5", "0", "7", "5", "5", "0", "9", "3", "7", "1", "1", "9", "4", "4", "9", "1", "3", "8", "2", "1", "6", "8" ]
[ "nonn", "cons", "easy" ]
15
0
1
[ "A006130", "A049310", "A052533", "A188943", "A209927", "A223139", "A356033" ]
null
Wolfdieter Lang, Aug 29 2022
2023-12-31T00:28:09
oeisdata/seq/A356/A356033.seq
c64b542e82889753107c8817436c54c9
A356034
Decimal expansion of the real root of x^3 - x^2 - 3.
[ "1", "8", "6", "3", "7", "0", "6", "5", "2", "7", "8", "1", "9", "1", "8", "9", "0", "9", "3", "2", "4", "1", "4", "6", "7", "9", "1", "5", "2", "7", "0", "3", "5", "9", "0", "0", "4", "2", "3", "1", "5", "4", "8", "8", "4", "2", "7", "0", "4", "1", "5", "3", "0", "2", "0", "0", "4", "4", "5", "5", "8", "0", "7", "3", "3", "4", "7", "4", "9", "2", "8", "2", "6", "7", "1", "8", "8", "7", "5", "0", "5", "3", "8", "4", "9", "3", "1", "1", "6", "7", "3" ]
[ "nonn", "cons", "easy" ]
19
1
2
[ "A356034", "A357100" ]
null
Wolfdieter Lang, Sep 13 2022
2022-11-09T04:39:07
oeisdata/seq/A356/A356034.seq
7939d4340f8b1c03b175a4c8070539ca
A356035
Decimal expansion of the real root of x^3 - 2*x^2 - 1.
[ "2", "2", "0", "5", "5", "6", "9", "4", "3", "0", "4", "0", "0", "5", "9", "0", "3", "1", "1", "7", "0", "2", "0", "2", "8", "6", "1", "7", "7", "8", "3", "8", "2", "3", "4", "2", "6", "3", "7", "7", "1", "0", "8", "9", "1", "9", "5", "9", "7", "6", "9", "9", "4", "4", "0", "4", "7", "0", "5", "5", "2", "2", "0", "3", "5", "5", "1", "8", "3", "4", "7", "9", "0", "3", "5", "9", "1", "6", "7", "4", "6", "9", "1", "7", "6", "4", "1", "8" ]
[ "nonn", "cons", "easy" ]
35
1
1
[ "A137421", "A272874", "A289265", "A356035", "A376121" ]
null
Wolfdieter Lang, Aug 18 2022
2024-12-04T11:41:02
oeisdata/seq/A356/A356035.seq
539dc5ba66eaa8e5f95ae21744844eda
A356036
Triangle read by rows, giving in the first column the powers of 3 (A000244) and in the next columns 4/3 times the previous row entry.
[ "1", "3", "4", "9", "12", "16", "27", "36", "48", "64", "81", "108", "144", "192", "256", "243", "324", "432", "576", "768", "1024", "729", "972", "1296", "1728", "2304", "3072", "4096", "2187", "2916", "3888", "5184", "6912", "9216", "12288", "16384", "6561", "8748", "11664", "15552", "20736", "27648", "36864", "49152", "65536", "19683", "26244", "34992", "46656", "62208", "82944", "110592", "147456", "196608", "262144" ]
[ "nonn", "tabl", "easy" ]
17
0
2
[ "A000244", "A000302", "A002001", "A002063", "A003946", "A005061", "A118265", "A257970", "A356036" ]
null
Wolfdieter Lang, Aug 01 2022
2022-08-05T13:15:39
oeisdata/seq/A356/A356036.seq
9bd53e9c9b9f0ad2bf1db0613f172ffb
A356037
Conjecturally, a(n) is the smallest number m such that every natural number is a sum of at most m n-simplex numbers.
[ "1", "3", "5", "8", "10", "13", "15", "15", "19", "24" ]
[ "nonn", "hard", "more" ]
22
1
2
[ "A000217", "A000292", "A000332", "A000389", "A000579", "A000580", "A000581", "A000582", "A002804", "A061336", "A079611", "A104246", "A283365", "A283370", "A356037" ]
null
Mohammed Yaseen, Jul 24 2022
2022-10-11T14:10:28
oeisdata/seq/A356/A356037.seq
40494f6bf624641ed96a1b5fba3a7b55
A356038
a(n) = Sum_{k=1..n} binomial(n,k) * sigma_2(k).
[ "1", "7", "28", "95", "286", "802", "2143", "5519", "13807", "33762", "81060", "191678", "447396", "1032647", "2360593", "5351231", "12041764", "26920297", "59829006", "132262550", "290990077", "637429514", "1390811841", "3023647046", "6551547161", "14151910442", "30481920523", "65480947739", "140318385088", "299995596747" ]
[ "nonn" ]
17
1
2
[ "A001157", "A006218", "A024916", "A064602", "A064603", "A160399", "A185003", "A356038", "A356039" ]
null
Vaclav Kotesovec, Jul 24 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356038.seq
2dee02ef1a3371659c5a60bff86830ca
A356039
a(n) = Sum_{k=1..n} binomial(n,k) * sigma_3(k).
[ "1", "11", "58", "243", "866", "2804", "8485", "24387", "67333", "180086", "469338", "1196976", "2996956", "7385837", "17954243", "43125267", "102494548", "241309031", "563341508", "1305142418", "3002938045", "6866090880", "15609292379", "35299794600", "79443050541", "177989130174", "397124963671", "882642816697", "1954708794400" ]
[ "nonn" ]
14
1
2
[ "A001158", "A006218", "A024916", "A064602", "A064603", "A160399", "A185003", "A356038", "A356039" ]
null
Vaclav Kotesovec, Jul 24 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356039.seq
3efc92a1087b4f27b66f149077715caf
A356040
a(n) is the smallest integer that has exactly n odious divisors (A227872) and n evil divisors (A356018).
[ "3", "6", "12", "24", "48", "96", "192", "210", "252", "528", "3072", "420", "12288", "2112", "1008", "840", "196608", "2016", "786432", "1680", "4032", "33792", "12582912", "3360", "30000", "135168", "16128", "6720", "805306368", "19152", "3221225472", "13440", "64512", "2162688", "120000", "26880", "206158430208", "8650752", "258048", "31920" ]
[ "nonn", "base" ]
38
1
1
[ "A000069", "A001969", "A005179", "A227872", "A230851", "A356018", "A356040" ]
null
Bernard Schott, Jul 24 2022
2022-07-26T10:10:01
oeisdata/seq/A356/A356040.seq
3eb095cb6cb54dfa94496e6e088b89b5
A356041
Numerator of the permanent of the matrix [m(j,k)]_{j,k=0..2*n}, where m(j,k) is 1 or (j+k)/(j-k) according as j = k or not.
[ "1", "-10", "5870", "-436619903", "204409938157631", "-445211270783816444430983", "396293055917701185511708646165266818589", "-50075241686736491417389691481681057226117081701278447", "5775845962974711619751142332219720943292883679628990682130802753216873" ]
[ "sign" ]
34
0
2
[ "A204249", "A356041" ]
null
Zhi-Wei Sun, Jul 24 2022
2022-08-27T08:13:04
oeisdata/seq/A356/A356041.seq
008765eb0a05ec70ba601f4b91736ebc
A356042
a(n) = Sum_{k=1..n} sigma_2(k) * floor(n/k).
[ "1", "7", "18", "45", "72", "138", "189", "301", "403", "565", "688", "985", "1156", "1462", "1759", "2212", "2503", "3115", "3478", "4207", "4768", "5506", "6037", "7269", "7947", "8973", "9895", "11272", "12115", "13897", "14860", "16678", "18031", "19777", "21154", "23908", "25279", "27457", "29338", "32362", "34045", "37411", "39262", "42583" ]
[ "nonn" ]
15
1
2
[ "A000005", "A007433", "A356042", "A356045" ]
null
Seiichi Manyama, Jul 24 2022
2022-08-07T04:07:52
oeisdata/seq/A356/A356042.seq
0528f579935294d450cb782624a22684
A356043
a(n) = Sum_{k=1..n} sigma_3(k) * floor(n/k).
[ "1", "11", "40", "123", "250", "540", "885", "1553", "2339", "3609", "4942", "7349", "9548", "12998", "16681", "22030", "26945", "34805", "41666", "52207", "62212", "75542", "87711", "107083", "122961", "144951", "166177", "194812", "219203", "256033", "285826", "328624", "367281", "416431", "460246", "525484", "576139", "644749", "708520" ]
[ "nonn" ]
14
1
2
[ "A000005", "A321140", "A356043", "A356045" ]
null
Seiichi Manyama, Jul 24 2022
2022-08-07T04:15:02
oeisdata/seq/A356/A356043.seq
670b3d7d45c20ef22e62c479c7cfd81d
A356044
Table read by antidiagonals: T(n,k) (n >= 3, k >= 1) is the number of regions formed in a regular n-gon by straight line segments when connecting the n corner vertices to the points dividing the sides into k equal parts.
[ "1", "6", "4", "19", "32", "11", "30", "96", "90", "24", "61", "188", "316", "246", "50", "78", "332", "580", "672", "462", "80", "127", "460", "1081", "1476", "1590", "856", "154", "150", "712", "1510", "2442", "2982", "2688", "1476", "220", "217", "916", "2306", "3528", "5370", "5504", "4861", "2420", "375", "246", "1204", "2930", "5310", "7742", "9440", "9288", "7360", "3630", "444" ]
[ "nonn", "tabl" ]
47
3
2
[ "A007678", "A092098", "A108914", "A356044" ]
null
Scott R. Shannon, Jul 31 2022
2022-08-17T10:14:48
oeisdata/seq/A356/A356044.seq
059accb92b110e97298b6cc6f1aa7243
A356045
Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} sigma_k(j) * floor(n/j).
[ "1", "1", "4", "1", "5", "7", "1", "7", "10", "13", "1", "11", "18", "21", "16", "1", "19", "40", "45", "28", "25", "1", "35", "102", "123", "72", "48", "28", "1", "67", "280", "393", "250", "138", "57", "38", "1", "131", "798", "1371", "1020", "540", "189", "83", "44", "1", "259", "2320", "5025", "4498", "2514", "885", "301", "101", "53", "1", "515", "6822", "18963", "20652", "12828", "4917", "1553", "403", "129", "56" ]
[ "nonn", "tabl" ]
21
1
3
[ "A061201", "A280077", "A322103", "A356042", "A356043", "A356045", "A356046" ]
null
Seiichi Manyama, Jul 24 2022
2022-07-25T15:41:31
oeisdata/seq/A356/A356045.seq
e02c6abd49fa8cf86bdd330f5ead2c3f
A356046
a(n) = Sum_{k=1..n} sigma_n(k) * floor(n/k).
[ "1", "7", "40", "393", "4498", "68898", "1205205", "24830617", "574911611", "14936215765", "427782762142", "13426870089265", "457622727372932", "16842615801316402", "665489035541044561", "28102162770144986248", "1262904298391426474369", "60182778141796948356895" ]
[ "nonn" ]
17
1
2
[ "A321141", "A356045", "A356046" ]
null
Seiichi Manyama, Jul 24 2022
2022-08-07T03:54:38
oeisdata/seq/A356/A356046.seq
199d0d45758987adbc29bf9cc42f5f74
A356047
The number of links of a qualifying "snake" polyline that connects the midpoints of opposite sides of the n-th regular integer hexagon that allows such a construction.
[ "2", "3", "44", "45", "626", "627", "8732", "8733", "121634", "121635", "1694156", "1694157", "23596562", "23596563", "328657724", "328657725", "4577611586", "4577611587", "63757904492", "63757904493", "888033051314", "888033051315", "12368704813916", "12368704813917", "172273834343522", "172273834343523", "2399464975995404", "2399464975995405", "33420235829592146", "33420235829592147" ]
[ "nonn", "easy" ]
46
1
1
[ "A001353", "A356047", "A357733" ]
null
Alexander M. Domashenko, Jul 24 2022
2025-01-31T11:51:11
oeisdata/seq/A356/A356047.seq
ac30fb14b253f56eed8f7b434d7e5235
A356048
a(n) is the least prime p such that p^2 - 2*prime(n)^2 is prime.
[ "5", "5", "11", "11", "17", "19", "29", "31", "37", "43", "53", "53", "61", "61", "67", "101", "97", "89", "97", "107", "109", "131", "127", "131", "139", "151", "149", "163", "157", "163", "181", "193", "199", "197", "227", "223", "223", "233", "257", "263", "263", "271", "271", "281", "293", "283", "317", "317", "347", "331", "331", "349", "349", "359", "367", "379", "389", "409", "431", "401", "409", "419", "449" ]
[ "nonn" ]
14
1
1
[ "A001248", "A356048", "A356060" ]
null
J. M. Bergot and Robert Israel, Jul 24 2022
2022-07-25T09:13:24
oeisdata/seq/A356/A356048.seq
902d1fae7d18d941d9c3e6381caaeeec
A356049
Symmetric array read by antidiagonals: T(n,k) is the number of legal positions in Go on an n X k board.
[ "1", "5", "5", "15", "57", "15", "41", "489", "489", "41", "113", "4125", "12675", "4125", "113", "313", "35117", "321689", "321689", "35117", "313", "867", "299681", "8180343", "24318165", "8180343", "299681", "867", "2401", "2557605", "208144601", "1840058693", "1840058693", "208144601", "2557605", "2401" ]
[ "nonn", "tabl" ]
46
1
2
[ "A094777", "A102620", "A266278", "A356049", "A356134" ]
null
Douglas Boffey, Jul 24 2022
2022-07-28T09:22:10
oeisdata/seq/A356/A356049.seq
b6595dd5731132e7dc1e40b1e682b5f5
A356050
a(n) = 2*A135318(n+1) - A135318(n).
[ "1", "1", "3", "4", "5", "6", "11", "14", "21", "26", "43", "54", "85", "106", "171", "214", "341", "426", "683", "854", "1365", "1706", "2731", "3414", "5461", "6826", "10923", "13654", "21845", "27306", "43691", "54614", "87381", "109226", "174763", "218454", "349525", "436906", "699051", "873814", "1398101", "1747626", "2796203", "3495254", "5592405" ]
[ "nonn", "easy" ]
61
0
3
[ "A001045", "A084214", "A094958", "A135318", "A230096", "A356050" ]
null
Paul Curtz, Aug 19 2022
2023-01-25T09:39:32
oeisdata/seq/A356/A356050.seq
8a45ec0bc14702ec94b5fc459a3faf74
A356051
a(n) is the index of the start of the first run of exactly n identical values in A356048.
[ "5", "1", "103", "2683", "2831", "22031", "9105296" ]
[ "nonn", "more" ]
15
1
1
[ "A356048", "A356051" ]
null
J. M. Bergot and Robert Israel, Jul 24 2022
2022-08-03T10:51:24
oeisdata/seq/A356/A356051.seq
013f3e27c024409fe4c93de94631a11e
A356052
Intersection of A001951 and A137803.
[ "1", "5", "7", "9", "11", "15", "19", "21", "22", "24", "26", "28", "32", "36", "38", "42", "45", "49", "53", "55", "57", "59", "63", "65", "66", "70", "72", "74", "76", "80", "82", "84", "86", "89", "91", "93", "97", "101", "103", "107", "111", "114", "118", "120", "124", "128", "130", "132", "135", "137", "141", "145", "147", "149", "151", "155", "156", "158", "162", "164" ]
[ "nonn", "easy" ]
10
1
2
[ "A001951", "A001952", "A136803", "A137804", "A356052", "A356053", "A356054", "A356055", "A356056", "A356081" ]
null
Clark Kimberling, Jul 26 2022
2025-03-23T03:20:58
oeisdata/seq/A356/A356052.seq
25bcaa0c9cc0df7555445df78d24692d
A356053
Intersection of A001951 and A137804.
[ "2", "4", "8", "12", "14", "16", "18", "25", "29", "31", "33", "35", "39", "41", "43", "46", "48", "50", "52", "56", "60", "62", "67", "69", "73", "77", "79", "83", "87", "90", "94", "96", "98", "100", "104", "106", "108", "110", "113", "115", "117", "121", "123", "125", "127", "131", "134", "138", "140", "142", "144", "148", "152", "154", "159", "161", "165", "169", "171" ]
[ "nonn", "easy" ]
4
1
1
[ "A001951", "A001952", "A136803", "A137804", "A356052", "A356053", "A356054", "A356055", "A356056" ]
null
Clark Kimberling, Jul 26 2022
2022-07-26T13:41:26
oeisdata/seq/A356/A356053.seq
5f559057e881c51f265078dee639426d
A356054
Intersection of A001952 and A137803.
[ "3", "13", "17", "30", "34", "40", "44", "47", "51", "61", "68", "78", "88", "95", "99", "105", "109", "112", "116", "122", "126", "133", "139", "143", "153", "160", "170", "174", "187", "191", "204", "208", "218", "225", "235", "245", "252", "256", "262", "266", "269", "273", "279", "283", "290", "300", "310", "317", "327", "331", "334", "338", "344", "348" ]
[ "nonn", "easy" ]
5
1
1
[ "A001951", "A001952", "A136803", "A137804", "A356052", "A356054", "A356055", "A356056" ]
null
Clark Kimberling, Jul 26 2022
2022-07-26T13:41:35
oeisdata/seq/A356/A356054.seq
507355627339539bbd87bbe2714c7cb3
A356055
Intersection of A001952 and A137804.
[ "6", "10", "20", "23", "27", "37", "54", "58", "64", "71", "75", "81", "85", "92", "102", "119", "129", "136", "146", "150", "157", "163", "167", "177", "180", "184", "194", "198", "201", "211", "215", "221", "228", "232", "238", "242", "249", "259", "276", "286", "293", "297", "303", "307", "314", "320", "324", "341", "351", "355", "358", "368", "372", "378", "385" ]
[ "nonn", "easy" ]
4
1
1
[ "A001951", "A001952", "A136803", "A137804", "A356052", "A356053", "A356055", "A356056", "A356081" ]
null
Clark Kimberling, Jul 26 2022
2022-07-26T13:41:44
oeisdata/seq/A356/A356055.seq
68079240c8c3e4ecaead992c52f43f95
A356056
a(n) = A001951(A137803(n)).
[ "1", "4", "7", "9", "12", "15", "18", "21", "24", "26", "29", "31", "33", "36", "39", "42", "45", "48", "50", "53", "56", "59", "62", "63", "66", "69", "72", "74", "77", "80", "83", "86", "89", "91", "93", "96", "98", "101", "104", "107", "110", "113", "115", "118", "121", "124", "125", "128", "131", "134", "137", "140", "142", "145", "148", "151", "154", "156", "158", "161" ]
[ "nonn", "easy" ]
12
1
2
[ "A001951", "A001952", "A136803", "A137804", "A356052", "A356056", "A356057", "A356058", "A356059" ]
null
Clark Kimberling, Jul 26 2022
2025-03-23T03:20:55
oeisdata/seq/A356/A356056.seq
998c7b7d13c990e18ed5546ba2fec814
A356057
a(n) = A001951(A137804(n)).
[ "2", "5", "8", "11", "14", "16", "19", "22", "25", "28", "32", "35", "38", "41", "43", "46", "49", "52", "55", "57", "60", "65", "67", "70", "73", "76", "79", "82", "84", "87", "90", "94", "97", "100", "103", "106", "108", "111", "114", "117", "120", "123", "127", "130", "132", "135", "138", "141", "144", "147", "149", "152", "155", "159", "162", "165", "168", "171", "173" ]
[ "nonn", "easy" ]
6
1
1
[ "A001951", "A001952", "A136803", "A137804", "A356052", "A356056", "A356057", "A356058", "A356059" ]
null
Clark Kimberling, Jul 26 2022
2022-08-03T23:27:40
oeisdata/seq/A356/A356057.seq
5c8778654d34dedc62fd18ac6fc87e0c
A356058
a(n) = A001952(A137803(n)).
[ "3", "10", "17", "23", "30", "37", "44", "51", "58", "64", "71", "75", "81", "88", "95", "102", "109", "116", "122", "129", "136", "143", "150", "153", "160", "167", "174", "180", "187", "194", "201", "208", "215", "221", "225", "232", "238", "245", "252", "259", "266", "273", "279", "286", "293", "300", "303", "310", "317", "324", "331", "338", "344", "351", "358" ]
[ "nonn", "easy" ]
16
1
1
[ "A001951", "A001952", "A136803", "A137804", "A356052", "A356056", "A356057", "A356058", "A356059" ]
null
Clark Kimberling, Jul 26 2022
2022-08-03T09:13:02
oeisdata/seq/A356/A356058.seq
73f9b19f5c9e3eb8eb138c5a66ad5970
A356059
a(n) = A001952(A137804(n)).
[ "6", "13", "20", "27", "34", "40", "47", "54", "61", "68", "78", "85", "92", "99", "105", "112", "119", "126", "133", "139", "146", "157", "163", "170", "177", "184", "191", "198", "204", "211", "218", "228", "235", "242", "249", "256", "262", "269", "276", "283", "290", "297", "307", "314", "320", "327", "334", "341", "348", "355", "361", "368", "375", "385", "392" ]
[ "nonn", "easy" ]
6
1
1
[ "A001951", "A001952", "A136803", "A137804", "A356052", "A356056", "A356057", "A356058", "A356059" ]
null
Clark Kimberling, Jul 26 2022
2022-08-03T23:27:54
oeisdata/seq/A356/A356059.seq
6f19a83954a4446e10b28c9b53a3720e
A356060
a(n) is the least prime p such that 2*prime(n)^2 + p is the square of a prime.
[ "17", "7", "71", "23", "47", "23", "263", "239", "311", "167", "887", "71", "359", "23", "71", "4583", "2447", "479", "431", "1367", "1223", "4679", "2351", "1319", "503", "2399", "983", "3671", "887", "1031", "503", "2927", "2063", "167", "7127", "4127", "431", "1151", "10271", "9311", "5087", "7919", "479", "4463", "8231", "887", "11447", "1031", "17351", "4679", "983", "7559", "5639", "2879", "2591" ]
[ "nonn" ]
17
1
1
[ "A001248", "A356048", "A356060" ]
null
J. M. Bergot and Robert Israel, Jul 24 2022
2022-08-04T05:04:25
oeisdata/seq/A356/A356060.seq
c1b35f23800a2cf9b22ca21fbffbcdd0
A356061
Numbers whose sum of digits is a refactorable number.
[ "1", "2", "8", "9", "10", "11", "17", "18", "20", "26", "27", "35", "36", "39", "44", "45", "48", "53", "54", "57", "62", "63", "66", "71", "72", "75", "80", "81", "84", "90", "93", "99", "100", "101", "107", "108", "110", "116", "117", "125", "126", "129", "134", "135", "138", "143", "144", "147", "152", "153", "156", "161", "162", "165", "170", "171", "174", "180", "183", "189", "192", "198", "200" ]
[ "nonn", "base", "easy" ]
44
1
2
[ "A000005", "A007953", "A033950", "A306509", "A356061", "A356520" ]
null
Ctibor O. Zizka, Aug 10 2022
2022-08-23T10:09:50
oeisdata/seq/A356/A356061.seq
e7a9fb62f71a02f5cf9b11c53d0e7155
A356062
a(n) is the smallest integer that has exactly n Lucas divisors (A000032).
[ "1", "2", "4", "12", "36", "252", "2772", "52668", "1211364", "35129556", "1089016236", "44649665676", "2098534286772", "417608323067628", "88115356167269508", "24760415083002731748", "7948093241643876891108", "4140956578896459860267268" ]
[ "nonn", "more" ]
30
1
2
[ "A000032", "A087997", "A129655", "A304092", "A333456", "A356062", "A356063" ]
null
Bernard Schott, Jul 25 2022
2022-08-31T13:31:00
oeisdata/seq/A356/A356062.seq
7a49b922695086fb27b29b45601a141c
A356063
a(n) is the new Lucas divisor that appears at the step A356062(n).
[ "1", "2", "4", "3", "18", "7", "11", "76", "322", "29", "1364", "123", "47", "199", "24476", "843", "5778", "521" ]
[ "nonn", "more" ]
11
1
2
[ "A000032", "A304092", "A349100", "A356062", "A356063" ]
null
Bernard Schott, Jul 25 2022
2022-08-31T13:32:04
oeisdata/seq/A356/A356063.seq
0e0518af745d270cf565b9db6611b68d
A356064
Numbers with a prime index other than 1 that is not a prime-power. Complement of A302492.
[ "13", "26", "29", "37", "39", "43", "47", "52", "58", "61", "65", "71", "73", "74", "78", "79", "86", "87", "89", "91", "94", "101", "104", "107", "111", "113", "116", "117", "122", "129", "130", "137", "139", "141", "142", "143", "145", "146", "148", "149", "151", "156", "158", "163", "167", "169", "172", "173", "174", "178", "181", "182", "183", "185", "188", "193" ]
[ "nonn" ]
7
1
1
[ "A000688", "A000961", "A001222", "A023893", "A023894", "A034699", "A050361", "A054685", "A076610", "A085970", "A106244", "A164336", "A246655", "A302492", "A302493", "A302601", "A330946", "A354911", "A355742", "A355743", "A356064", "A356065", "A356066" ]
null
Gus Wiseman, Jul 25 2022
2022-07-29T09:51:20
oeisdata/seq/A356/A356064.seq
496001a822243d0f16950432f99f8339
A356065
Squarefree numbers whose prime indices are all prime-powers.
[ "1", "3", "5", "7", "11", "15", "17", "19", "21", "23", "31", "33", "35", "41", "51", "53", "55", "57", "59", "67", "69", "77", "83", "85", "93", "95", "97", "103", "105", "109", "115", "119", "123", "127", "131", "133", "155", "157", "159", "161", "165", "177", "179", "187", "191", "201", "205", "209", "211", "217", "227", "231", "241", "249", "253", "255", "265", "277" ]
[ "nonn" ]
6
1
2
[ "A000688", "A000961", "A001222", "A001970", "A005117", "A023893", "A023894", "A034699", "A050361", "A054685", "A055887", "A063834", "A076610", "A106244", "A164336", "A246655", "A279784", "A279786", "A295935", "A296131", "A302492", "A302493", "A302496", "A302590", "A302601", "A355731", "A355741", "A355742", "A355743", "A355744", "A356064", "A356065", "A356066" ]
null
Gus Wiseman, Jul 25 2022
2022-07-29T09:51:24
oeisdata/seq/A356/A356065.seq
e75b02af65cc5b97035d1fdbc835fed5
A356066
Numbers with a prime index that is not a prime-power. Complement of A355743.
[ "2", "4", "6", "8", "10", "12", "13", "14", "16", "18", "20", "22", "24", "26", "28", "29", "30", "32", "34", "36", "37", "38", "39", "40", "42", "43", "44", "46", "47", "48", "50", "52", "54", "56", "58", "60", "61", "62", "64", "65", "66", "68", "70", "71", "72", "73", "74", "76", "78", "79", "80", "82", "84", "86", "87", "88", "89", "90", "91", "92", "94", "96", "98", "100", "101" ]
[ "nonn" ]
6
1
1
[ "A000688", "A000961", "A001222", "A023894", "A034699", "A050361", "A054685", "A076610", "A085970", "A106244", "A164336", "A246655", "A302492", "A302493", "A302601", "A330946", "A354911", "A355742", "A355743", "A356064", "A356065", "A356066" ]
null
Gus Wiseman, Jul 31 2022
2022-08-01T08:21:24
oeisdata/seq/A356/A356066.seq
0490a8d3cba228c11c75f7950367dbb5
A356067
Number of integer partitions of n into relatively prime prime-powers.
[ "0", "0", "0", "0", "0", "1", "0", "3", "2", "5", "4", "11", "7", "18", "16", "26", "27", "43", "41", "65", "65", "92", "100", "137", "142", "194", "210", "270", "295", "379", "410", "519", "571", "699", "782", "947", "1046", "1267", "1414", "1673", "1870", "2213", "2465", "2897", "3230", "3757", "4210", "4871", "5427", "6265", "6997" ]
[ "nonn" ]
6
0
8
[ "A000009", "A000041", "A000688", "A000961", "A001970", "A023893", "A023894", "A050361", "A054685", "A055887", "A063834", "A072233", "A076610", "A085970", "A106244", "A164336", "A246655", "A279784", "A289509", "A354911", "A355737", "A355742", "A355743", "A356065", "A356067" ]
null
Gus Wiseman, Jul 28 2022
2022-07-29T09:51:27
oeisdata/seq/A356/A356067.seq
943f57c49b77e4eddd4cfca3a2324bc6
A356068
Number of integers ranging from 1 to n that are not prime-powers (1 is not a prime-power).
[ "1", "1", "1", "1", "1", "2", "2", "2", "2", "3", "3", "4", "4", "5", "6", "6", "6", "7", "7", "8", "9", "10", "10", "11", "11", "12", "12", "13", "13", "14", "14", "14", "15", "16", "17", "18", "18", "19", "20", "21", "21", "22", "22", "23", "24", "25", "25", "26", "26", "27", "28", "29", "29", "30", "31", "32", "33", "34", "34", "35", "35", "36", "37", "37", "38", "39", "39", "40", "41", "42" ]
[ "nonn" ]
8
1
6
[ "A000688", "A000720", "A000961", "A001222", "A023894", "A025528", "A036234", "A050361", "A054685", "A062298", "A065515", "A065855", "A069513", "A085970", "A143731", "A164336", "A246655", "A355743", "A356064", "A356065", "A356066", "A356068" ]
null
Gus Wiseman, Jul 31 2022
2022-08-01T08:21:02
oeisdata/seq/A356/A356068.seq
d3acece85d6ba32b6b58290b7029240c
A356069
Number of divisors of n whose prime indices cover an interval of positive integers (A073491).
[ "1", "2", "2", "3", "2", "4", "2", "4", "3", "3", "2", "6", "2", "3", "4", "5", "2", "6", "2", "4", "3", "3", "2", "8", "3", "3", "4", "4", "2", "7", "2", "6", "3", "3", "4", "9", "2", "3", "3", "5", "2", "5", "2", "4", "6", "3", "2", "10", "3", "4", "3", "4", "2", "8", "3", "5", "3", "3", "2", "10", "2", "3", "4", "7", "3", "5", "2", "4", "3", "5", "2", "12", "2", "3", "6", "4", "4", "5", "2", "6", "5", "3", "2", "7", "3", "3" ]
[ "nonn" ]
8
1
2
[ "A000005", "A001222", "A001223", "A028334", "A029709", "A055874", "A055932", "A056239", "A070824", "A073491", "A073492", "A112798", "A119313", "A137921", "A287170", "A307516", "A328338", "A356069", "A356223", "A356224", "A356225", "A356226", "A356233", "A356237" ]
null
Gus Wiseman, Aug 28 2022
2022-08-30T09:41:22
oeisdata/seq/A356/A356069.seq
92d3d56236e94de117a05ee3dfbe1f66
A356070
Number of astronomical units (A163103) in a light-year (A213614).
[ "6", "3", "2", "4", "1", "0", "7", "7", "0", "8", "4", "2", "6", "6", "2", "8", "0", "2", "6", "8", "6", "5", "3", "5", "8", "3", "1", "8", "2", "3", "1", "7", "3", "1", "3", "5", "5", "7", "8", "5", "9", "3", "4", "9", "9", "3", "2", "5", "7", "8", "9", "5", "3", "4", "7", "8", "3", "7", "9", "9", "5", "6", "6", "4", "7", "3", "3", "7", "4", "9", "4", "4", "9", "0", "1", "5", "3", "8", "6", "2", "8", "6", "5", "1", "0", "8", "2", "7", "9", "9", "1" ]
[ "nonn", "cons", "easy" ]
16
5
1
[ "A003678", "A163103", "A213614", "A230979", "A356070" ]
null
Jianing Song, Jul 25 2022
2022-07-25T22:42:54
oeisdata/seq/A356/A356070.seq
54279d182d34b3a70fdfe23956640606
A356071
Numbers whose square is in A108571.
[ "1", "20864888", "23309765", "146095088", "725027284", "745400258", "803458304", "810273142", "816409484", "1663345356", "2970502211", "5035530306", "5705842932", "5801143392", "5969549784", "6143081912", "6582975516", "6801076116", "6828208884", "6830325216", "6911416408", "7248217206", "7248822984", "7317408465" ]
[ "nonn", "fini", "base" ]
13
1
2
[ "A108571", "A181392", "A225886", "A356071", "A356072" ]
null
Jianing Song, Jul 25 2022
2022-07-25T10:44:07
oeisdata/seq/A356/A356071.seq
020457838516a91791fc0e32b8ae8328
A356072
Cubes in A108571.
[ "1", "63727566782531668573568877888875", "49731947369965677347595574679599669", "51677995937349669479966437557564799", "56739945449541793697765966999776573", "76997569379457651594939677645469973", "578489779534895499899488878979775533", "788899738636778969999897877368221696" ]
[ "nonn", "base", "fini" ]
11
1
2
[ "A108571", "A181392", "A225886", "A356071", "A356072" ]
null
Jianing Song, Jul 25 2022
2022-07-25T08:24:30
oeisdata/seq/A356/A356072.seq
1e073897a75a774bb8d8725bded2686c
A356073
Number of labeled trees on [n] having a centroid.
[ "0", "1", "0", "3", "4", "125", "486", "16807", "118784", "4782969", "50781250", "2357947691", "33981990912", "1792160394037", "32942263538380", "1946195068359375", "43756164738973696", "2862423051509815793" ]
[ "nonn" ]
15
0
4
[ "A000272", "A027416", "A356073", "A356186" ]
null
Geoffrey Critzer, Jul 31 2022
2022-08-04T15:54:36
oeisdata/seq/A356/A356073.seq
28586e10d41cdff008e4036afa5f54c9
A356074
a(n) is the first prime that starts a sequence of exactly n consecutive primes prime(k+1), ..., prime(k+n) where prime(k+i)+2^i is prime for i = 1...n but not for i = n+1.
[ "3", "11", "17", "5", "37307", "17387", "87020177", "1309757957" ]
[ "nonn", "more" ]
9
1
1
null
null
J. M. Bergot and Robert Israel, Jul 31 2022
2022-08-13T15:52:43
oeisdata/seq/A356/A356074.seq
37f831fcbda866d8a6364f54449aa95e
A356075
a(n) = floor(m), where li(m) = n and li is the logarithmic integral. We consider only real and positive m.
[ "1", "2", "4", "5", "7", "9", "11", "14", "17", "20", "23", "26", "29", "33", "36", "40", "44", "48", "52", "56", "60", "64", "68", "72", "77", "81", "85", "90", "94", "99", "104", "108", "113", "118", "122", "127", "132", "137", "142", "147", "152", "157", "162", "167", "172", "178", "183", "188", "193", "198", "204", "209", "214", "220", "225", "231", "236", "242", "247", "253", "258" ]
[ "nonn" ]
26
1
2
[ "A052435", "A089963", "A096353", "A223853", "A337734", "A337735", "A356075" ]
null
Thomas Scheuerle, Jul 25 2022
2022-10-08T10:12:48
oeisdata/seq/A356/A356075.seq
cdde76d59e0aaa917a12a25d93e334dc
A356076
a(n) = Sum_{k=1..n} sigma_k(k) * floor(n/k).
[ "1", "7", "36", "315", "3442", "50926", "874471", "17717759", "405157961", "10414927743", "295726598356", "9214021189459", "312089127781714", "11424774177252514", "449318695090042077", "18896344248088180470", "846136606134424944649", "40192694877626991357901" ]
[ "nonn" ]
22
1
2
[ "A023887", "A344434", "A356046", "A356076" ]
null
Seiichi Manyama, Jul 25 2022
2024-09-08T14:51:43
oeisdata/seq/A356/A356076.seq
00fc644ed232c748312384a47c506b63
A356077
a(n) is the least prime p such that 2*n - p^2 is prime, or -1 if there is no such p.
[ "-1", "-1", "2", "-1", "-1", "3", "3", "3", "-1", "3", "3", "-1", "3", "3", "5", "3", "-1", "5", "3", "3", "5", "5", "3", "5", "3", "3", "5", "3", "-1", "7", "3", "-1", "5", "3", "3", "5", "-1", "3", "5", "3", "3", "5", "5", "3", "7", "3", "-1", "5", "3", "-1", "7", "5", "3", "5", "3", "3", "5", "3", "3", "7", "3", "11", "5", "5", "-1", "5", "5", "3", "5", "3", "-1", "11", "3", "3", "7", "5", "-1", "5", "3", "3", "5", "5", "3", "11", "-1", "3", "5", "3", "-1", "7", "3", "-1" ]
[ "sign" ]
28
1
3
[ "A005384", "A356077", "A356108" ]
null
J. M. Bergot and Robert Israel, Jul 27 2022
2022-07-28T12:52:18
oeisdata/seq/A356/A356077.seq
3bc676736a26363f69af10bc87384fa8
A356078
Highly composite numbers that are multiples of their number of divisors.
[ "1", "2", "12", "24", "36", "60", "180", "240", "360", "720", "1260", "1680", "5040", "10080", "15120", "20160", "25200", "55440", "110880", "221760", "277200", "665280", "720720", "1441440", "2882880", "3603600", "8648640", "14414400", "32432400", "43243200", "61261200", "245044800", "551350800", "735134400", "1102701600", "2205403200" ]
[ "nonn" ]
7
1
2
[ "A002182", "A002183", "A033950", "A356078" ]
null
J. Lowell, Jul 25 2022
2022-08-24T09:58:13
oeisdata/seq/A356/A356078.seq
1fb9218092f39d0c0ced10ce6d13eccb
A356079
Primes p such that p+6, p-6, 2*p+3 and 2*p-3 are prime.
[ "13", "17", "53", "67", "157", "563", "613", "647", "1187", "1453", "1663", "4007", "4133", "5443", "5743", "6073", "6863", "7823", "8747", "11833", "12113", "12583", "12653", "15467", "21997", "23747", "25463", "25673", "26183", "41017", "42683", "59447", "60337", "65173", "67427", "68443", "75527", "80783", "89527", "94433", "95917", "100517", "101203", "104003", "110603", "111773" ]
[ "nonn" ]
11
1
1
null
null
J. M. Bergot and Robert Israel, Jul 25 2022
2022-08-03T11:45:25
oeisdata/seq/A356/A356079.seq
297eaa3ae5638549c734f7db4a91ecdb
A356080
Variation on Recamán's sequence (A005132) that is intended to be a permutation of the nonnegative integers, essentially as envisaged by the original comments in A078943. See comments below for details.
[ "0", "1", "3", "6", "2", "7", "13", "20", "28", "37", "27", "16", "4", "17", "31", "46", "30", "47", "29", "48", "68", "89", "111", "134", "158", "133", "159", "132", "160", "131", "101", "70", "38", "5", "39", "74", "110", "147", "109", "148", "108", "149", "107", "150", "106", "151", "105", "58", "10", "59", "9", "60", "8", "61", "115", "170", "226", "283", "341", "400", "460", "399", "337", "274", "210", "145", "79", "12", "80", "11" ]
[ "nonn" ]
34
1
3
[ "A005132", "A078943", "A356080" ]
null
Peter Munn, Jul 25 2022
2024-08-07T15:11:14
oeisdata/seq/A356/A356080.seq
3deda32480050edc43210cc2695b9c38
A356081
Numbers k such that A356052(k) = A356056(k).
[ "1", "3", "4", "6", "8", "14", "16", "17", "22", "25", "27", "28", "30", "38", "40", "67", "68", "74", "78", "82", "102", "104", "109", "110", "112", "126", "128", "132", "136", "140", "160", "164", "188" ]
[ "nonn", "fini" ]
4
1
2
[ "A001951", "A137803", "A137804", "A356052", "A356056", "A356081" ]
null
Clark Kimberling, Jul 26 2022
2022-08-03T23:28:03
oeisdata/seq/A356/A356081.seq
f9fd753270ec72cd068292ebcde21955
A356082
Matula-Goebel number of the complete binary tree of n levels.
[ "1", "4", "49", "51529", "400034745289", "135016053798647886015597889" ]
[ "nonn", "more" ]
9
1
2
[ "A006894", "A084107", "A356082", "A356083", "A356084" ]
null
Kevin Ryde, Jul 26 2022
2022-07-26T16:04:59
oeisdata/seq/A356/A356082.seq
40edb7443cd0b66daf8a4de96193da95
A356083
Matula-Goebel number of the complete ternary tree of n levels.
[ "1", "8", "6859", "328951971956791", "1658040970678649782777422161327743110829397625479" ]
[ "nonn", "more" ]
8
1
2
[ "A007097", "A356082", "A356083", "A356084" ]
null
Kevin Ryde, Jul 27 2022
2022-07-28T17:00:32
oeisdata/seq/A356/A356083.seq
1f1956d45b5f8018e049ff710a6e46ea
A356084
Matula-Goebel number of the complete quaternary (4-ary) tree of n levels.
[ "1", "16", "7890481", "379723559137648771815613388050801" ]
[ "nonn", "more" ]
6
1
2
[ "A007097", "A356082", "A356083", "A356084" ]
null
Kevin Ryde, Jul 27 2022
2022-07-27T10:36:22
oeisdata/seq/A356/A356084.seq
b470880b04710aae8a0dc918e3fdce6f
A356085
Intersection of A001951 and A054406.
[ "2", "4", "7", "9", "11", "14", "16", "18", "21", "26", "28", "33", "35", "42", "49", "52", "56", "59", "63", "66", "70", "73", "80", "82", "87", "89", "94", "97", "101", "104", "106", "108", "111", "113", "115", "118", "120", "123", "125", "127", "130", "132", "134", "137", "141", "144", "149", "151", "156", "158", "165", "172", "175", "179", "182", "186", "189", "196" ]
[ "nonn", "easy" ]
5
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356085", "A356086", "A356087", "A356088" ]
null
Clark Kimberling, Jul 26 2022
2022-08-03T23:28:12
oeisdata/seq/A356/A356085.seq
292e1cc15fdc4ae7ecb00f4344b0ea2f
A356086
Intersection of A001952 and A022838.
[ "3", "6", "10", "13", "17", "20", "27", "34", "51", "58", "64", "71", "81", "88", "95", "102", "105", "109", "112", "116", "119", "122", "126", "129", "133", "136", "143", "150", "157", "174", "180", "187", "204", "211", "218", "221", "225", "228", "232", "235", "242", "245", "249", "252", "256", "259", "266", "273", "284", "285", "287", "289", "290", "292", "294" ]
[ "nonn", "easy" ]
11
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356085", "A356086", "A356087", "A356088" ]
null
Clark Kimberling, Aug 04 2022
2022-08-06T19:07:20
oeisdata/seq/A356/A356086.seq
adc84c40f4f99f208e185ed2d0a8cb79
A356087
Intersection of A001952 and A054406.
[ "23", "30", "37", "40", "44", "47", "54", "61", "68", "75", "78", "85", "92", "99", "139", "146", "153", "160", "163", "167", "170", "177", "184", "191", "194", "198", "201", "208", "215", "238", "262", "269", "276", "279", "283", "286", "288", "291", "293", "295", "298", "300", "302", "305", "307", "309", "312", "314", "317", "319", "321", "324", "326", "328" ]
[ "nonn", "easy" ]
7
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356085", "A356086", "A356087", "A356088" ]
null
Clark Kimberling, Aug 04 2022
2022-08-05T07:42:26
oeisdata/seq/A356/A356087.seq
f346e2e87560de7ca10e8200fb5e772b
A356088
a(n) = A001951(A022838(n)).
[ "1", "4", "7", "8", "11", "14", "16", "18", "21", "24", "26", "28", "31", "33", "35", "38", "41", "43", "45", "48", "50", "53", "55", "57", "60", "63", "65", "67", "70", "72", "74", "77", "80", "82", "84", "87", "90", "91", "94", "97", "100", "101", "104", "107", "108", "111", "114", "117", "118", "121", "124", "127", "128", "131", "134", "135", "138", "141", "144", "145" ]
[ "nonn", "easy" ]
21
1
2
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356088", "A356089", "A356090", "A356091" ]
null
Clark Kimberling, Aug 04 2022
2025-04-13T01:46:00
oeisdata/seq/A356/A356088.seq
66d85ecd7b49c8414f0b6ee71d785fb0
A356089
a(n) = A001951(A054406(n)).
[ "2", "5", "9", "12", "15", "19", "22", "25", "29", "32", "36", "39", "42", "46", "49", "52", "56", "59", "62", "66", "69", "73", "76", "79", "83", "86", "89", "93", "96", "98", "103", "106", "110", "113", "115", "120", "123", "125", "130", "132", "137", "140", "142", "147", "149", "152", "156", "159", "162", "166", "169", "173", "176", "179", "183", "186", "189", "193" ]
[ "nonn", "easy" ]
19
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356088", "A356089", "A356090", "A356091" ]
null
Clark Kimberling, Aug 04 2022
2025-03-23T04:33:18
oeisdata/seq/A356/A356089.seq
d03c284f74517b65d0fb4941e0d830f2
A356090
a(n) = A001952(A022838(n)).
[ "3", "10", "17", "20", "27", "34", "40", "44", "51", "58", "64", "68", "75", "81", "85", "92", "99", "105", "109", "116", "122", "129", "133", "139", "146", "153", "157", "163", "170", "174", "180", "187", "194", "198", "204", "211", "218", "221", "228", "235", "242", "245", "252", "259", "262", "269", "276", "283", "286", "293", "300", "307", "310", "317", "324" ]
[ "nonn", "easy" ]
17
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356088", "A356089", "A356090", "A356091" ]
null
Clark Kimberling, Aug 04 2022
2025-03-23T04:34:16
oeisdata/seq/A356/A356090.seq
af0bde0cd6e907a40900b34d0e7c6f80
A356091
a(n) = A001952(A054406(n)).
[ "6", "13", "23", "30", "37", "47", "54", "61", "71", "78", "88", "95", "102", "112", "119", "126", "136", "143", "150", "160", "167", "177", "184", "191", "201", "208", "215", "225", "232", "238", "249", "256", "266", "273", "279", "290", "297", "303", "314", "320", "331", "338", "344", "355", "361", "368", "378", "385", "392", "402", "409", "419", "426", "433" ]
[ "nonn", "easy" ]
14
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356088", "A356089", "A356090", "A356091" ]
null
Clark Kimberling, Aug 05 2022
2025-03-23T04:34:53
oeisdata/seq/A356/A356091.seq
a621c1c4b5393c5b715f00600e118cf8
A356092
Decimal expansion of the imaginary part of the first nontrivial zero of zeta'.
[ "2", "3", "2", "9", "8", "3", "2", "0", "4", "9", "2", "7", "6", "2", "8", "5", "7", "9", "0", "2", "0", "1", "0", "9", "6", "1", "6", "2", "6", "5", "9", "7", "8", "4", "7", "0", "5", "0", "5", "9", "5", "7", "6", "3", "9", "0", "0", "2", "8", "8", "3", "4", "9", "0", "2", "1", "4", "3", "0", "6", "9", "0", "4", "1", "0", "2", "8", "8", "6", "9", "2", "0", "7", "8", "2", "5", "0", "8", "9", "3", "9", "2", "6", "2", "4", "4", "5", "2", "4", "1", "3", "2", "4", "7", "0", "3", "5", "4", "3", "6", "6", "3", "2", "7", "8", "9", "8", "7", "7", "2", "1", "2", "1", "7", "7", "2", "7", "4", "5", "9", "5", "6", "3", "1", "6", "6", "1" ]
[ "nonn", "cons" ]
40
2
1
[ "A356092", "A356216" ]
null
Benoit Cloitre, Aug 13 2022
2022-08-15T05:13:53
oeisdata/seq/A356/A356092.seq
1bd6c77a919981ea039a7b5f4b2ee3a9
A356093
a(n) = numerator((prime(n)-1)/prime(n)#), where prime(n)# = A002110(n) is the n-th primorial.
[ "1", "1", "2", "1", "1", "2", "8", "3", "1", "2", "1", "6", "4", "1", "1", "2", "1", "2", "1", "1", "12", "1", "1", "4", "16", "10", "1", "1", "18", "8", "3", "1", "4", "1", "2", "5", "2", "27", "1", "2", "1", "6", "1", "32", "14", "3", "1", "1", "1", "2", "4", "1", "8", "25", "128", "1", "2", "9", "2", "4", "1", "2", "3", "1", "4", "2", "1", "8", "1", "2", "16", "1", "1", "2", "9", "1", "2", "6", "40", "4", "1", "2", "1" ]
[ "nonn", "frac" ]
15
1
3
[ "A002110", "A006093", "A038110", "A039787", "A053669", "A249270", "A338559", "A340818", "A341431", "A342450", "A342479", "A356093", "A356094" ]
null
Amiram Eldar, Jul 26 2022
2022-07-30T08:18:43
oeisdata/seq/A356/A356093.seq
a6aef9ff884103aa354eaf3210cc12fa
A356094
a(n) = denominator((prime(n)-1)/prime(n)#), where prime(n)# = A002110(n) is the n-th primorial.
[ "2", "3", "15", "35", "231", "5005", "255255", "1616615", "10140585", "462120945", "6685349671", "1236789689135", "30425026352721", "311494317420715", "13367169186706335", "1253429172199617105", "33151040519900217915", "3909612711980232366109", "119065478046670712967865", "7970583287524270870963077" ]
[ "nonn", "frac" ]
14
1
1
[ "A002110", "A038111", "A338560", "A340819", "A341432", "A342451", "A342480", "A356093", "A356094" ]
null
Amiram Eldar, Jul 26 2022
2022-07-30T08:18:39
oeisdata/seq/A356/A356094.seq
880cc4901e376e3199de3e3e61ccb69d
A356095
Tetrahedral numbers which are products of three distinct primes.
[ "165", "286", "455", "969", "1771", "4495", "9139", "12341", "32509", "176851", "437989", "657359", "939929", "3737581", "9290431", "21084251", "26536591", "39338069", "44101441", "61690919", "92568571", "112805879", "289442201", "381588019", "439918931", "495593039", "711215371", "815946449", "1008077071", "1103914379" ]
[ "nonn" ]
12
1
1
[ "A000292", "A007304", "A070755", "A356095" ]
null
Massimo Kofler, Jul 26 2022
2025-03-10T12:26:35
oeisdata/seq/A356/A356095.seq
80cfc6ed24b974e21aec68c056b9e8dd
A356096
A family of triangles T(m), m >= 0, read by triangles and then by rows; triangle T(0) is [1; 1, 1]; for m >= 0, triangle T(m+1) is obtained by replacing each subtriangle [t; u, v] in T(m) by [t; 2*t-u, 2*t-v; 2*u-t, t+u+v, 2*v-t; u, 2*u-v, 2*v-u, v].
[ "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "-1", "5", "-1", "1", "1", "5", "5", "5", "5", "1", "1", "-1", "5", "3", "5", "-1", "1", "1", "1", "5", "5", "5", "5", "1", "1", "1", "3", "1", "-1", "5", "-1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "-1", "5", "-1", "1" ]
[ "sign", "tabf" ]
11
0
8
[ "A355855", "A356002", "A356096", "A356097", "A356098" ]
null
Rémy Sigrist, Jul 26 2022
2023-01-18T03:28:47
oeisdata/seq/A356/A356096.seq
0263f4d7a2d9caec9bf4756d7b216888
A356097
A family of triangles T(m), m >= 0, read by triangles and then by rows; triangle T(0) is [1; 1, 1]; for m >= 0, triangle T(m+1) is obtained by replacing each subtriangle [t; u, v] in T(m) by [t; t, t; u, t+u+v, v; u, u, v, v].
[ "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "5", "3", "3", "5", "1", "1", "1", "3", "3", "3", "1", "1", "1", "1", "5", "3", "3", "5", "1", "1", "1", "3", "1", "1", "5", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "5", "3", "3", "5", "1" ]
[ "nonn", "tabf" ]
12
0
8
[ "A353174", "A355855", "A356002", "A356096", "A356097", "A356098" ]
null
Rémy Sigrist, Jul 26 2022
2023-01-18T03:28:43
oeisdata/seq/A356/A356097.seq
a24c8ecc6b427520e7196c49d0d15f07
A356098
A family of triangles T(m), m >= 0, read by triangles and then by rows; triangle T(0) is [1; 1, 1]; for m >= 0, triangle T(m+1) is obtained by replacing each subtriangle [t; u, v] in T(m) by [t; t-u, t-v; u-t, t+u+v, v-t; u, u-v, v-u, v].
[ "1", "1", "1", "1", "0", "0", "0", "3", "0", "1", "0", "0", "1", "1", "1", "1", "-1", "1", "-1", "0", "0", "0", "0", "0", "-3", "3", "-3", "0", "0", "3", "3", "3", "3", "0", "0", "-3", "3", "3", "3", "-3", "0", "-1", "0", "3", "3", "3", "3", "0", "-1", "1", "1", "0", "-3", "3", "-3", "0", "1", "1", "1", "1", "-1", "0", "0", "0", "0", "-1", "1", "1", "1", "0", "0", "0", "3", "0", "1", "0", "0", "1", "2", "0", "3", "0", "2" ]
[ "sign", "tabl" ]
10
0
8
[ "A355855", "A356002", "A356096", "A356097", "A356098" ]
null
Rémy Sigrist, Jul 26 2022
2023-01-18T03:28:59
oeisdata/seq/A356/A356098.seq
468764cd448215e11da5111ec550f7d9
A356099
E.g.f. satisfies A(x) = 1/(1 - x)^(x^3 * A(x)).
[ "1", "0", "0", "0", "24", "60", "240", "1260", "68544", "604800", "5508000", "54885600", "1877420160", "32069157120", "499522645440", "7832035411200", "236207887534080", "5868136834560000", "133085307920947200", "2941187195765145600", "91568561750088652800", "2857211689810118860800" ]
[ "nonn" ]
21
0
5
[ "A353229", "A356099", "A356911" ]
null
Seiichi Manyama, Sep 03 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356099.seq
8ce94e1c124a041331204be197d209db
A356100
a(n) = Sum_{k=1..n} (k - 1)^n * floor(n/k).
[ "0", "1", "9", "99", "1301", "20581", "376891", "7914216", "186905206", "4915451602", "142368695176", "4506118905870", "154720069309364", "5729167232515112", "227585086051159866", "9654819212943764500", "435659280972794395356", "20836049921760968809231", "1052864549462731148832219" ]
[ "nonn" ]
19
1
3
[ "A121706", "A236632", "A319194", "A332469", "A356100" ]
null
Seiichi Manyama, Jul 26 2022
2024-12-14T12:24:34
oeisdata/seq/A356/A356100.seq
d902aceac3ee8ae8cf99e723f3930a90