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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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A364301
a(n) = [x^n] 1/(1 + x) * Legendre_P(n, (1 - x)/(1 + x))^(-n) for n >= 0.
[ "1", "1", "73", "10805", "3100001", "1479318759", "1062573281785", "1073267499046525", "1451614640844881665", "2534009926232394596267", "5548110762587726241026801", "14890865228866506199602545427", "48084585660733078332263158771313", "183923731031112887024255817209295155", "822427361894711201025101782425695273529" ]
[ "nonn", "easy" ]
8
0
3
[ "A005258", "A005259", "A108625", "A143007", "A364116", "A364298", "A364301", "A364302" ]
null
Peter Bala, Jul 18 2023
2023-07-20T10:09:50
oeisdata/seq/A364/A364301.seq
ae9a3541eb9496d4a400a991d58b65a8
A364302
a(n) = [x^n] 1/(1 + x) * Legendre_P(n, (1 - x)/(1 + x))^(-n-1) for n >= 0.
[ "1", "3", "163", "23623", "6751251", "3219777011", "2313306332191", "2337707082109071", "3163417897474821763", "5524913023443862515019", "12101947272421487464092429", "32493996621780038121738419591", "104964758754905547830609842389527", "401618040258524641485654323795309235" ]
[ "nonn", "easy" ]
6
0
2
[ "A364117", "A364298", "A364301", "A364302" ]
null
Peter Bala, Jul 18 2023
2023-07-20T10:10:07
oeisdata/seq/A364/A364302.seq
2439ddbec0bce944af49338990b4bc4a
A364303
Square array read by ascending antidiagonals: T(n,k) = [x^k] (1 - x)^(2*k) * Legendre_P(n*k, (1 + x)/(1 - x)) for n, k >= 0.
[ "1", "1", "-2", "1", "0", "6", "1", "4", "-6", "-20", "1", "10", "36", "0", "70", "1", "18", "300", "400", "90", "-252", "1", "28", "1050", "11440", "4900", "0", "924", "1", "40", "2646", "77616", "485100", "63504", "-1680", "-3432", "1", "54", "5544", "316540", "6370650", "21841260", "853776", "0", "12870", "1", "70", "10296", "972400", "42031990", "554822268", "1022041020", "11778624", "34650", "-48620" ]
[ "sign", "tabl", "easy" ]
17
0
3
[ "A000984", "A002894", "A245086", "A275652", "A275653", "A275654", "A275655", "A364113", "A364298", "A364303", "A364304", "A364305" ]
null
Peter Bala, Jul 19 2023
2023-07-24T15:09:46
oeisdata/seq/A364/A364303.seq
9cfbf231af53f7814e06ca4ec5395d03
A364304
a(n) = (7*n)!*(9*n/2)!*(5*n/2)!/((5*n)!*(7*n/2)!^2*n!^2).
[ "1", "54", "10296", "2484000", "665091000", "188907932304", "55737530929080", "16888537352985408", "5218680924762089400", "1637124203403474142500", "519752205290081232622296", "166620892958456148158454144", "53846423260084127389865311800" ]
[ "nonn", "easy" ]
27
0
2
[ "A275652", "A275654", "A364303", "A364304" ]
null
Peter Bala, Jul 21 2023
2023-10-07T06:59:07
oeisdata/seq/A364/A364304.seq
4c79b3d7c31adb7240b01490a0f956a4
A364305
a(n) = (8*n)!*(5*n)!*(3*n)! / ( (6*n)!*(4*n)!^2*n!^2 ).
[ "1", "70", "17550", "5567380", "1960044750", "732012601320", "283986961467300", "113142133870180800", "45969979122504907470", "18961650930856541865100", "7915377251895103264073800", "3336455614603881320759754000", "1417729131896719482585245182500", "606517077508008639090614765297280" ]
[ "nonn", "easy" ]
26
0
2
[ "A001449", "A211421", "A364303", "A364305" ]
null
Peter Bala, Jul 21 2023
2024-10-31T01:35:25
oeisdata/seq/A364/A364305.seq
427eb1230b71fa566a6c0939725e1073
A364306
Number of free asymmetrical polyhexes with n cells.
[ "0", "0", "0", "2", "10", "57", "279", "1338", "6329", "29969", "142461", "680637", "3269716", "15785281", "76557773", "372812193", "1822122394", "8934639920", "43938614933", "216649723022", "1070790651782", "5303849549438", "26323051151997", "130878360554692", "651812916543553", "3251215337590494", "16240020424411300", "81227146998545009", "406770969279959357", "2039375194931563287" ]
[ "nonn" ]
14
1
4
[ "A000228", "A001207", "A006535", "A030225", "A030226", "A364306" ]
null
John Mason, Jul 18 2023
2023-08-26T02:50:11
oeisdata/seq/A364/A364306.seq
c3209a06acd322f5f502d9f91e134574
A364307
Numbers k such that k, k+1 and k+2 have exactly 2 distinct prime factors.
[ "20", "33", "34", "38", "44", "50", "54", "55", "56", "74", "75", "85", "86", "91", "92", "93", "94", "98", "115", "116", "117", "122", "133", "134", "141", "142", "143", "144", "145", "146", "158", "159", "160", "175", "176", "183", "187", "200", "201", "205", "206", "207", "212", "213", "214", "215", "216", "217", "224", "235", "247", "248", "295", "296" ]
[ "nonn" ]
18
1
1
[ "A001221", "A006073", "A039833", "A074851", "A364265", "A364266", "A364307", "A364308", "A364309" ]
null
R. J. Mathar, Jul 18 2023
2025-05-12T10:01:36
oeisdata/seq/A364/A364307.seq
2bd56120c54370b7db2d64f28e094468
A364308
Numbers k such that k, k+1 and k+2 have exactly 3 distinct prime factors.
[ "644", "740", "804", "986", "1034", "1064", "1104", "1220", "1274", "1308", "1309", "1462", "1494", "1580", "1748", "1884", "1885", "1924", "1988", "2013", "2014", "2108", "2134", "2254", "2288", "2294", "2330", "2354", "2364", "2408", "2464", "2484", "2540", "2583", "2584", "2664", "2665", "2666", "2678", "2684", "2714", "2715", "2716", "2754", "2793" ]
[ "nonn" ]
20
1
1
[ "A001221", "A006073", "A080569", "A140077", "A364265", "A364266", "A364307", "A364308", "A364309" ]
null
R. J. Mathar, Jul 18 2023
2024-10-01T03:33:18
oeisdata/seq/A364/A364308.seq
ae7c57d1250d9c0ee9c0ba726ac708a0
A364309
Numbers k such that k, k+1 and k+2 have exactly 4 distinct prime factors.
[ "37960", "44484", "45694", "50140", "51428", "55130", "55384", "61334", "63364", "64294", "67164", "68264", "68474", "70004", "70090", "71708", "72708", "76152", "80444", "81548", "81718", "82040", "84434", "85490", "86240", "90363", "95380", "97382", "98020", "99084", "99384", "99428", "99788", "100164", "100490", "100594", "102254", "102542", "104804", "105994", "108204" ]
[ "nonn" ]
19
1
1
[ "A001221", "A006073", "A087966", "A140078", "A168628", "A176167", "A364265", "A364266", "A364307", "A364308", "A364309" ]
null
R. J. Mathar, Jul 18 2023
2024-10-01T03:05:54
oeisdata/seq/A364/A364309.seq
e40006f5540d5204a1dbc5c9f76e6845
A364310
Number T(n,k) of partitions of n into k parts where each block of part i with multiplicity j is marked with a word of length i*j over an n-ary alphabet whose letters appear in alphabetical order and all n letters occur exactly once in the partition; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
[ "1", "0", "1", "0", "1", "1", "0", "1", "3", "1", "0", "1", "5", "6", "1", "0", "1", "15", "15", "10", "1", "0", "1", "22", "76", "35", "15", "1", "0", "1", "63", "168", "252", "70", "21", "1", "0", "1", "93", "574", "785", "658", "126", "28", "1", "0", "1", "255", "2188", "3066", "2739", "1470", "210", "36", "1", "0", "1", "386", "5490", "18235", "12181", "7857", "2940", "330", "45", "1" ]
[ "nonn", "tabl" ]
18
0
9
[ "A000007", "A000012", "A000217", "A000332", "A057427", "A178682", "A364285", "A364310" ]
null
Alois P. Heinz, Jul 18 2023
2023-11-18T07:27:25
oeisdata/seq/A364/A364310.seq
76ff0d7b6e2730be343678352a0d691e
A364311
Lexicographically earliest infinite sequence of nonnegative integers, {a(n)} for n>=0, such that all lines with equations y = a(n)*x + n are in general position.
[ "0", "1", "3", "2", "5", "4", "8", "11", "6", "13", "12", "7", "22", "16", "17", "21", "9", "14", "10", "27", "18", "15", "19", "28", "31", "43", "34", "38", "23", "39", "25", "36", "41", "20", "55", "63", "42", "30", "24", "33", "26", "32", "65", "66", "51", "59", "29", "56", "35", "62", "85", "81", "37", "49", "46", "68", "74", "78", "88", "48", "44", "75", "40", "47", "97", "76", "93", "79", "92", "54", "58", "100", "61", "101", "107", "52" ]
[ "nonn" ]
52
0
3
[ "A000217", "A364311" ]
null
Luc Rousseau, Sep 22 2023
2023-10-08T09:56:49
oeisdata/seq/A364/A364311.seq
aa2676f4c33d47c80359a82419ff2e10
A364312
Irregular triangle T read by rows, giving in row n the nonnegative coefficients of polynomials of height n and degree k (of decreasing powers), for k = 1, 2, ..., n-1, used for Cantor's counting of algebraic numbers, written for m = 1, 2, ..., A364313(n), for n >= 2, and for n = 1 the degree is k = 1.
[ "1", "0", "1", "1", "2", "1", "1", "2", "1", "0", "1", "3", "1", "1", "3", "2", "0", "1", "1", "0", "2", "1", "1", "1", "4", "1", "1", "4", "3", "2", "2", "3", "3", "0", "1", "1", "0", "3", "2", "1", "1", "1", "2", "1", "1", "1", "2", "2", "0", "0", "1", "1", "0", "0", "2", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "5", "1", "1", "5", "4", "0", "1", "1", "0", "4", "3", "0", "2", "2", "0", "3", "3", "1", "1", "1", "3", "1", "1", "1", "3", "2", "2", "1", "2", "1", "2", "1", "2", "2" ]
[ "nonn", "tabf" ]
22
1
5
[ "A000051", "A001227", "A001622", "A005409", "A364312", "A364313", "A364314", "A364315", "A364316" ]
null
Wolfdieter Lang, Jul 19 2023
2023-07-22T12:38:26
oeisdata/seq/A364/A364312.seq
7868fd723a46e6b9bebefbb025ba2687
A364313
Length of row n of the irregular triangle A364312.
[ "2", "2", "7", "13", "44", "95", "231" ]
[ "nonn", "more" ]
12
1
1
[ "A364312", "A364313" ]
null
Wolfdieter Lang, Jul 19 2023
2023-07-23T18:23:36
oeisdata/seq/A364/A364313.seq
74090bd78974ec89ee1674eb9e094a7f
A364314
Number of polynomials (with nonnegative coefficients) of Cantor's height n and degree k (in the range {1, 2, ..., n-1}), for n >= 2; and for n = 1 the degree is k = 1.
[ "1", "1", "3", "5", "14", "26", "57" ]
[ "nonn", "more" ]
14
1
3
[ "A364312", "A364313", "A364314" ]
null
Wolfdieter Lang, Jul 19 2023
2023-07-27T08:28:39
oeisdata/seq/A364/A364314.seq
4047805919ef7fa827f3ac6967b9e8a6
A364315
Irregular triangle T read by rows obtained from A364312. Row n gives the number of real algebraic numbers from the (also signed) polynomials of Cantor's height n, and degree k, for k = 1, 2, ..., n-1, for n >= 2, and for n = 1 the degree is 1.
[ "1", "2", "4", "0", "4", "8", "0", "8", "8", "12", "0", "4", "32", "20", "16", "0", "12", "28", "100", "16", "16", "0" ]
[ "nonn", "tabf", "more" ]
11
1
2
[ "A028310", "A364312", "A364313", "A364314", "A364315", "A364316" ]
null
Wolfdieter Lang, Jul 19 2023
2023-07-22T08:16:09
oeisdata/seq/A364/A364315.seq
234b70489b88dab1942c80d648d881e1
A364316
Number of real algebraic numbers of Cantor's height n.
[ "1", "2", "4", "12", "28", "72", "172" ]
[ "nonn", "more" ]
5
1
2
[ "A364312", "A364315", "A364316" ]
null
Wolfdieter Lang, Jul 19 2023
2023-07-22T08:16:24
oeisdata/seq/A364/A364316.seq
d21fc2bcf344820ab13ef3278b910f20
A364317
Irregular triangle T read by rows: T(n, k) gives the number of permutations of [n] = {1, 2, ..., n} with a cycle of length m = floor(n/2) + k = A138099(n, k), for 1 <= k <= n - floor(n/2) = ceiling(n/2).
[ "1", "1", "3", "2", "8", "6", "40", "30", "24", "180", "144", "120", "1260", "1008", "840", "720", "8064", "6720", "5760", "5040", "72576", "60480", "51840", "45360", "40320", "604800", "518400", "453600", "403200", "362880", "6652800", "5702400", "4989600", "4435200", "3991680", "3628800" ]
[ "nonn", "tabf", "easy" ]
21
1
3
[ "A008619", "A058312", "A058313", "A119248", "A126074", "A138099", "A364317" ]
null
Wolfdieter Lang, Aug 12 2023
2023-09-25T18:22:37
oeisdata/seq/A364/A364317.seq
5031ab078f6ad5ce1a41499bd23450ed
A364318
Irregular table T read by rows: T(n,k) gives for permutations of [n] = {1, 2, ..., n}, n >= 1, the number of cycles corresponding to the k-th partition of n without part 1 (in Abramowitz-Stegun order).
[ "0", "1", "2", "6", "3", "24", "20", "120", "90", "40", "15", "720", "504", "420", "210", "5040", "3360", "2688", "1260", "1260", "1120", "105", "40320", "25920", "20160", "18144", "9072", "15120", "2240", "2520", "362880", "226800", "172800", "151200", "72576", "75600", "120960", "56700", "50400", "18900", "25200", "945" ]
[ "nonn", "tabf" ]
14
1
3
[ "A000142", "A000166", "A002865", "A008306", "A135573", "A364318" ]
null
Wolfdieter Lang, Aug 14 2023
2024-03-19T08:29:51
oeisdata/seq/A364/A364318.seq
f7aef69e3e297db0957079a541aecbc7
A364319
a(n) = (A077446(n) + 1)/2 for n >= 0.
[ "0", "1", "3", "6", "16", "33", "91", "190", "528", "1105", "3075", "6438", "17920", "37521", "104443", "218686", "608736", "1274593", "3547971", "7428870", "20679088", "43298625", "120526555", "252362878", "702480240", "1470878641", "4094354883", "8572908966", "23863649056", "49966575153", "139087539451" ]
[ "nonn", "easy" ]
24
0
3
[ "A001109", "A001541", "A006452", "A049310", "A077446", "A364319" ]
null
Wolfdieter Lang, Aug 15 2023
2023-09-25T07:51:19
oeisdata/seq/A364/A364319.seq
d35e1d06af256720e3dddac14c9848b4
A364320
Prime numbers that are the exact average of eight consecutive odd semiprimes.
[ "43", "317", "607", "719", "853", "887", "919", "1231", "1237", "1283", "1303", "1951", "2179", "2609", "3001", "3271", "3389", "3491", "3547", "3643", "3889", "3931", "4241", "4297", "4447", "4517", "4567", "4621", "4817", "4831", "4871", "4909", "5479", "5623", "5647", "5653", "5953", "6211", "6301", "6869", "7019", "7559", "8011", "8191", "8297", "8311", "8317", "8369", "8447" ]
[ "nonn" ]
30
1
1
[ "A000040", "A046315", "A363074", "A363187", "A363188", "A364147", "A364148", "A364149", "A364320", "A364321", "A364689" ]
null
Elmo R. Oliveira, Sep 25 2023
2023-10-09T18:37:43
oeisdata/seq/A364/A364320.seq
0775cdac5d88c601e576f8ba3623b5ed
A364321
Prime numbers that are the exact average of nine consecutive odd semiprimes.
[ "97", "191", "293", "347", "401", "409", "479", "727", "1823", "1931", "2063", "2089", "2897", "2903", "2999", "3061", "3083", "3119", "3571", "3617", "3673", "3727", "3967", "4339", "4373", "4583", "4639", "4703", "4813", "5297", "5347", "5437", "5639", "5821", "6047", "6053", "6311", "6421", "6491", "6529", "6761", "6883", "7283", "7417", "7451", "7949", "8059", "8123", "8237" ]
[ "nonn" ]
13
1
1
[ "A000040", "A046315", "A363074", "A363187", "A363188", "A364147", "A364148", "A364149", "A364320", "A364321", "A364689" ]
null
Elmo R. Oliveira, Sep 25 2023
2023-10-09T18:37:55
oeisdata/seq/A364/A364321.seq
fa4f2cdaa235c1ab30a220486428a7e1
A364322
Number of partitions of 2n with largest part n where each block of part i with multiplicity j is marked with a word of length i*j over a (2n)-ary alphabet whose letters appear in alphabetical order and all 2n letters occur exactly once in the partition.
[ "1", "1", "7", "81", "841", "10333", "137677", "1973401", "29150551", "484498301", "8769443541", "167200081777", "3311785261513", "66867027890601", "1437872937193801", "33031740883673521", "796918495251727081", "19807865344255857661", "501642119664087055501", "12828972405814319046601" ]
[ "nonn" ]
11
0
3
[ "A364285", "A364322" ]
null
Alois P. Heinz, Jul 18 2023
2023-07-20T09:42:31
oeisdata/seq/A364/A364322.seq
25e301ca0880d34c1286376bab69e291
A364323
Number of partitions of 2n into n parts where each block of part i with multiplicity j is marked with a word of length i*j over a (2n)-ary alphabet whose letters appear in alphabetical order and all 2n letters occur exactly once in the partition.
[ "1", "1", "5", "76", "785", "12181", "377708", "8009002", "171155505", "4073421919", "168532394115", "6213455777530", "198071252771780", "6383569557705276", "204582355050315856", "8766238064421938746", "446196770370016437201", "20584924968627941009331", "920598569147050035793061" ]
[ "nonn" ]
16
0
3
[ "A364310", "A364323" ]
null
Alois P. Heinz, Jul 18 2023
2023-11-29T05:59:52
oeisdata/seq/A364/A364323.seq
a63e7c01f9142be67074353abcb5474b
A364324
a(n) = n!*tribonacci(n+2).
[ "1", "1", "4", "24", "168", "1560", "17280", "221760", "3265920", "54069120", "994291200", "20118067200", "444034483200", "10617070464000", "273391121203200", "7542665754624000", "221969877921792000", "6940528784437248000", "229781192298577920000", "8030036368187817984000", "295390797322766745600000" ]
[ "nonn" ]
18
0
3
[ "A000073", "A000142", "A002866", "A005442", "A189886", "A364324" ]
null
Enrique Navarrete, Jul 18 2023
2023-08-31T02:58:46
oeisdata/seq/A364/A364324.seq
8d81ae81a635df10bc86391221478c6b
A364325
Underline the k-th digit of a(n), k being the leftmost digit of a(n). This is the lexicographically earliest sequence of distinct terms > 0 such that the succession of underlined digits is the succession of the sequence's digits themselves.
[ "1", "10", "20", "22", "200", "220", "221", "222", "201", "202", "223", "224", "203", "225", "226", "11", "227", "228", "229", "302", "204", "12", "312", "205", "322", "332", "342", "23", "352", "362", "24", "372", "206", "230", "382", "392", "25", "2200", "2201", "26", "13", "14", "2202", "2203", "27", "2204", "2205", "28", "2206", "2207", "29", "231", "207", "2208", "2209", "208", "240", "15", "2210", "232", "16", "2211" ]
[ "base", "nonn" ]
30
1
2
[ "A364325", "A364326" ]
null
Eric Angelini, Jul 18 2023
2023-10-23T18:53:05
oeisdata/seq/A364/A364325.seq
782906720b41bba3db294261cd6035db
A364326
Underline the k-th digit of a(n), k being the rightmost digit of a(n). This is the lexicographically earliest sequence of distinct terms > 0 such that the succession of the underlined digit is the succession of the sequence's digits themselves.
[ "1", "11", "101", "111", "102", "112", "121", "131", "141", "151", "202", "12", "161", "171", "21", "181", "22", "191", "212", "31", "312", "412", "41", "512", "612", "51", "712", "32", "302", "42", "812", "52", "912", "61", "1001", "1011", "71", "1013", "62", "1021", "1031", "81", "1041", "72", "82", "1051", "91", "1061", "92", "1071", "122", "103", "1081", "113", "1091", "201", "142", "1101", "211", "242" ]
[ "base", "nonn" ]
18
1
2
[ "A364325", "A364326" ]
null
Eric Angelini, Jul 18 2023
2023-10-23T18:53:30
oeisdata/seq/A364/A364326.seq
c22aa3588558f0626ed53e0a06146858
A364327
Number of endofunctions on [n] such that the number of elements that are mapped to i is either 0 or a divisor of i.
[ "1", "1", "3", "13", "115", "851", "13431", "144516", "2782571", "47046307", "1107742273", "19263747713", "657152726011", "13657313316986", "451605697223110", "13377063396461138", "531234399267707419", "14563460779785318719", "721703507708044677945", "22141894282020163910406", "1123287408943765640907425" ]
[ "nonn" ]
18
0
3
[ "A066843", "A178682", "A334370", "A364327", "A364328", "A364344" ]
null
Alois P. Heinz, Jul 18 2023
2023-07-20T10:38:47
oeisdata/seq/A364/A364327.seq
0e397ad63a0d39cb2391926fe6bf9b6c
A364328
Number of endofunctions on [n] such that the number of elements that are mapped to i is either 0 or a prime divisor of i.
[ "1", "0", "1", "1", "6", "21", "110", "904", "4312", "74400", "731412", "5600761", "128196024", "792051157", "18696610816", "264267572121", "7136433698464", "57948743342529", "2228312959187256", "22463157401776612", "681974906329502904", "15395459281239915282", "463374873030990445252", "6091833036158810701465" ]
[ "nonn" ]
15
0
5
[ "A000040", "A178682", "A334370", "A364327", "A364328", "A364344" ]
null
Alois P. Heinz, Jul 18 2023
2023-07-20T10:39:05
oeisdata/seq/A364/A364328.seq
130bad722d2f584e03782e135e43caf5
A364329
G.f. satisfies A(x) = (1 + x^3) * (1 + x*A(x)^2).
[ "1", "1", "2", "6", "17", "52", "167", "558", "1912", "6683", "23736", "85426", "310861", "1141837", "4227938", "15764474", "59140089", "223062670", "845388258", "3217750229", "12295043520", "47144444476", "181349473833", "699629022954", "2706327445312", "10494497061015", "40787775234746", "158859378070721" ]
[ "nonn", "easy" ]
18
0
3
[ "A073157", "A215576", "A364329", "A364330" ]
null
Seiichi Manyama, Jul 18 2023
2024-03-03T09:50:30
oeisdata/seq/A364/A364329.seq
9388d18d679df3e0989235ad05233ea7
A364330
G.f. satisfies A(x) = (1 + x^4) * (1 + x*A(x)^2).
[ "1", "1", "2", "5", "15", "45", "142", "464", "1556", "5327", "18532", "65326", "232826", "837589", "3037472", "11092143", "40753626", "150541422", "558762382", "2082871613", "7794301294", "29269317708", "110263451242", "416595676681", "1578183767068", "5993326380378", "22812048907856", "87010994947971", "332531385362972" ]
[ "nonn", "easy" ]
19
0
3
[ "A073157", "A215576", "A364329", "A364330" ]
null
Seiichi Manyama, Jul 18 2023
2024-03-03T09:50:26
oeisdata/seq/A364/A364330.seq
2eebf5812dc027731f6590b1d00c19f7
A364331
G.f. satisfies A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^5).
[ "1", "2", "15", "163", "2070", "28698", "421015", "6425644", "100977137", "1622885389", "26551709946", "440744175801", "7404449354076", "125657625548824", "2150963575012295", "37094953102567208", "643904274979347286", "11241232087809137759", "197247501440314516840", "3476787208220672891388", "61533794803235280779261" ]
[ "nonn", "easy" ]
23
0
2
[ "A007863", "A069271", "A073157", "A200719", "A215623", "A215624", "A215654", "A215715", "A239108", "A364331", "A364333", "A364335", "A364338" ]
null
Seiichi Manyama, Jul 18 2023
2025-03-27T23:27:45
oeisdata/seq/A364/A364331.seq
de3b6623aded854560018409fd10f5e6
A364332
a(n) = f(prime(n)), where f(2) = 0 and for an odd prime p, f(p) = max{f(q)+1: q ranges over all prime factors of p-1}.
[ "0", "1", "1", "2", "2", "2", "1", "2", "3", "3", "2", "2", "2", "3", "4", "3", "4", "2", "3", "3", "2", "3", "3", "3", "2", "2", "2", "4", "2", "3", "3", "3", "2", "4", "3", "2", "3", "2", "4", "4", "4", "2", "3", "2", "3", "3", "3", "3", "4", "3", "4", "3", "2", "2", "1", "4", "4", "2", "4", "3", "5", "3", "2", "3", "3", "4", "3", "3", "5", "4", "3", "5", "3", "3", "3", "4", "3", "3", "2", "2", "3", "3", "4", "2", "3", "3", "3", "3", "4", "3", "5", "4", "2", "3", "4", "3", "4", "3", "4" ]
[ "nonn" ]
45
1
4
[ "A082449", "A083647", "A364332", "A364334" ]
null
Steven Lu, Jul 18 2023
2025-03-27T23:27:41
oeisdata/seq/A364/A364332.seq
d32bca0145c8bf114038f7a3ddc14067
A364333
G.f. satisfies A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^6).
[ "1", "2", "17", "216", "3224", "52640", "910452", "16392140", "303996224", "5767278431", "111401778266", "2183535060362", "43319505976084", "868220464851417", "17552981176788200", "357544690982030744", "7330803752675100908", "151172599088871911072", "3133367418601958989295", "65242183918761533467216" ]
[ "nonn" ]
12
0
2
[ "A007863", "A069271", "A073157", "A200718", "A215654", "A215715", "A239109", "A364331", "A364333", "A364339", "A364340" ]
null
Seiichi Manyama, Jul 18 2023
2023-07-19T07:48:35
oeisdata/seq/A364/A364333.seq
7e437152bc34a3b84f3e7696d42b5979
A364334
a(2) = 0; a(n) = a(n-1) + 1 if n is an odd prime; otherwise a(n) = max{a(k) : k is divisor of n, 1 < k < n}.
[ "0", "1", "0", "1", "1", "2", "0", "1", "1", "2", "1", "2", "2", "1", "0", "1", "1", "2", "1", "2", "2", "3", "1", "1", "2", "1", "2", "3", "1", "2", "0", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "3", "2", "1", "3", "4", "1", "2", "1", "1", "2", "3", "1", "2", "2", "2", "3", "4", "1", "2", "2", "2", "0", "2", "2", "3", "1", "3", "2", "3", "1", "2", "2", "1", "2", "2", "2", "3", "1", "1", "2", "3", "2", "1", "3", "3", "2", "3", "1", "2", "3", "2", "4", "2", "1", "2", "2", "2", "1", "2", "1", "2", "2", "2", "3", "4", "1", "2", "2", "2", "2" ]
[ "nonn" ]
25
2
6
[ "A364332", "A364334" ]
null
Steven Lu, Jul 18 2023
2023-09-17T01:22:50
oeisdata/seq/A364/A364334.seq
2ff63b7aad121b55a6aeeb164e0c092c
A364335
G.f. satisfies A(x) = (1 + x*A(x)^3) * (1 + x*A(x)^5).
[ "1", "2", "17", "204", "2852", "43489", "701438", "11767095", "203223146", "3589167533", "64524575635", "1176860764416", "21723084076739", "405038036077647", "7617437252889030", "144328483391622298", "2752414654270742784", "52790626691557217602", "1017655117382823639414", "19706520281177438174530" ]
[ "nonn" ]
8
0
2
[ "A215624", "A234525", "A239108", "A364331", "A364335", "A364338" ]
null
Seiichi Manyama, Jul 18 2023
2023-07-19T07:48:27
oeisdata/seq/A364/A364335.seq
cde92feb3a0eb8ddc73830b9687360a2
A364336
G.f. satisfies A(x) = (1 + x) * (1 + x*A(x)^3).
[ "1", "2", "7", "39", "242", "1634", "11631", "85957", "653245", "5072862", "40077807", "321106623", "2602911282", "21308131235", "175909559897", "1462846379247", "12242600576066", "103035285071630", "871490142773640", "7404121610615520", "63157400073057627", "540689217572662413", "4644083121177225292" ]
[ "nonn" ]
23
0
2
[ "A073157", "A198953", "A212071", "A215623", "A215654", "A216359", "A364336", "A364337", "A364338", "A364339" ]
null
Seiichi Manyama, Jul 19 2023
2024-09-11T05:47:47
oeisdata/seq/A364/A364336.seq
2692b7350104affd069d93d72aa2573b
A364337
G.f. satisfies A(x) = (1 + x) * (1 + x*A(x)^4).
[ "1", "2", "9", "68", "580", "5406", "53270", "545844", "5757332", "62094217", "681653493", "7591431752", "85558696024", "974024788280", "11184192097016", "129378232148016", "1506363564912368", "17639001584452320", "207593804132718948", "2454236122156830254", "29132714097692056954", "347086786035103983446" ]
[ "nonn" ]
18
0
2
[ "A073157", "A215623", "A215715", "A234461", "A239107", "A364336", "A364337", "A364338", "A364339" ]
null
Seiichi Manyama, Jul 19 2023
2025-03-24T22:33:40
oeisdata/seq/A364/A364337.seq
d36a331678bb0e9de52587b4ee0007ad
A364338
G.f. satisfies A(x) = (1 + x) * (1 + x*A(x)^5).
[ "1", "2", "11", "105", "1140", "13555", "170637", "2235472", "30161255", "416248640", "5848462880", "83378361111", "1203100853951", "17537182300140", "257858115407535", "3819894878557990", "56958234329850060", "854192593184162160", "12875579347191388830", "194963091634569681550", "2964229359714424159370", "45234864131654311730160" ]
[ "nonn" ]
19
0
2
[ "A073157", "A215624", "A234525", "A239108", "A364331", "A364335", "A364336", "A364337", "A364338", "A364339" ]
null
Seiichi Manyama, Jul 19 2023
2025-03-24T22:33:44
oeisdata/seq/A364/A364338.seq
27bcdcc83f52d98467067b3e202fafe2
A364339
G.f. satisfies A(x) = (1 + x) * (1 + x*A(x)^6).
[ "1", "2", "13", "150", "1978", "28603", "438273", "6992052", "114915180", "1932233883", "33081722359", "574755965137", "10107627041697", "179576579730534", "3218352405778284", "58114340679967608", "1056284029850962674", "19310039426151335622", "354818596435147647654", "6549556302551204621664", "121394125733645986376838" ]
[ "nonn" ]
14
0
2
[ "A073157", "A239109", "A364333", "A364336", "A364337", "A364338", "A364339", "A364340" ]
null
Seiichi Manyama, Jul 19 2023
2025-03-24T22:34:04
oeisdata/seq/A364/A364339.seq
a3ccd8cc74aea2cbfe8b89505661dfe0
A364340
G.f. satisfies A(x) = (1 + x*A(x)) * (1 + x*A(x)^6).
[ "1", "2", "15", "179", "2502", "38262", "619991", "10459410", "181771289", "3231782239", "58505593456", "1074766446526", "19984671314164", "375414901633692", "7113886504446443", "135820770971898805", "2610186429457347486", "50452256583633573513", "980187901557594671335", "19130197594133100828170", "374894511736219913097375" ]
[ "nonn" ]
12
0
2
[ "A007863", "A198953", "A215623", "A215624", "A239109", "A364333", "A364339", "A364340" ]
null
Seiichi Manyama, Jul 19 2023
2023-07-19T07:48:38
oeisdata/seq/A364/A364340.seq
25787431288d1aca41674e57c8144eef
A364341
a(n) is the greatest k such that there are exactly n distinct numbers j that can be expressed as the sum of two squares with k^2 < j < (k+1)^2, or -1 if such a k does not exist.
[ "0", "1", "3", "4", "6", "7", "11", "10", "14", "12", "16", "20", "22", "23", "21", "27", "29", "30", "32", "35", "38", "37", "42", "44", "47", "43", "54", "52", "51", "58", "57", "62", "56", "71", "64", "67", "68", "73", "76", "77", "78", "83", "72", "87", "90", "91", "-1", "95", "103", "100", "107", "109", "105", "104", "108", "-1", "116", "119", "110", "129", "117", "126", "-1", "128", "134" ]
[ "sign" ]
7
0
3
[ "A077773", "A363761", "A363763", "A364341" ]
null
Rainer Rosenthal, Jul 20 2023
2023-07-30T13:33:21
oeisdata/seq/A364/A364341.seq
66bd3e93ab03bc020127b47e0d28ac5a
A364342
a(n) is the number of base-10 nonbouncy numbers below 10^n.
[ "10", "100", "475", "1675", "4954", "12952", "30817", "67987", "140907", "277033", "520565", "940455", "1641355", "2778305", "4576113", "7354549", "11560664", "17809754", "26936719", "40059819", "58659104", "84672094", "120609609", "169694999", "236030401", "324794055", "442473145", "597137095", "798756745", "1059575359" ]
[ "nonn", "base", "easy" ]
18
1
1
[ "A152054", "A204692", "A364342" ]
null
Peter Cullen Burbery, Jul 19 2023
2023-07-27T22:04:54
oeisdata/seq/A364/A364342.seq
600f37ac79d59d37488f37c75b996b71
A364343
Expansion of Sum_{k>0} k * x^k/(1 + x^k)^3.
[ "1", "-1", "9", "-12", "20", "-12", "35", "-60", "72", "-30", "77", "-132", "104", "-56", "210", "-256", "170", "-117", "209", "-320", "378", "-132", "299", "-672", "425", "-182", "594", "-588", "464", "-360", "527", "-1040", "858", "-306", "910", "-1224", "740", "-380", "1170", "-1640", "902", "-672", "989", "-1364", "1890", "-552", "1175", "-2928", "1470", "-775", "1938", "-1872", "1484", "-1080", "2090" ]
[ "sign" ]
32
1
3
[ "A002129", "A048272", "A309731", "A320900", "A364343", "A364351" ]
null
Seiichi Manyama, Jul 19 2023
2023-07-20T10:47:02
oeisdata/seq/A364/A364343.seq
8ac8bc77485b8a9e0904179ecbd6dad7
A364344
Number of endofunctions on [n] such that the number of elements that are mapped to i is a multiple or a divisor of i.
[ "1", "1", "4", "20", "177", "1462", "21919", "254802", "4816788", "82401465", "1929926410", "35256890748", "1152938630784", "24977973856643", "823036511854847", "24332827884557037", "954801492779273665", "27023410818058291822", "1309814517293654535339", "41375530521928893861920" ]
[ "nonn" ]
15
0
3
[ "A000312", "A178682", "A334370", "A364327", "A364328", "A364344" ]
null
Alois P. Heinz, Jul 19 2023
2023-10-27T12:20:41
oeisdata/seq/A364/A364344.seq
949111873f3edc4cd877814fbd722428
A364345
Number of integer partitions of n without any three parts (a,b,c) (repeats allowed) satisfying a + b = c. A variation of sum-free partitions.
[ "1", "1", "2", "2", "4", "5", "7", "10", "13", "16", "21", "27", "34", "43", "54", "67", "83", "102", "122", "151", "182", "218", "258", "313", "366", "443", "513", "611", "713", "844", "975", "1149", "1325", "1554", "1780", "2079", "2381", "2761", "3145", "3647", "4134", "4767", "5408", "6200", "7014", "8035", "9048", "10320", "11639", "13207", "14836", "16850" ]
[ "nonn" ]
15
0
3
[ "A000009", "A000041", "A002865", "A007865", "A008284", "A008289", "A025065", "A026905", "A093971", "A108917", "A111133", "A236912", "A237113", "A237667", "A240861", "A275972", "A288728", "A320340", "A320347", "A323092", "A325862", "A326083", "A363225", "A363226", "A363260", "A364345", "A364346", "A364347", "A364348" ]
null
Gus Wiseman, Jul 20 2023
2023-10-18T04:43:41
oeisdata/seq/A364/A364345.seq
1801f305eabeba0c12490648220c4bc4
A364346
Number of strict integer partitions of n such that there is no ordered triple of parts (a,b,c) (repeats allowed) satisfying a + b = c. A variation of sum-free strict partitions.
[ "1", "1", "1", "1", "2", "3", "2", "4", "4", "5", "5", "8", "9", "11", "11", "16", "16", "20", "20", "25", "30", "34", "38", "42", "50", "58", "64", "73", "80", "90", "105", "114", "128", "148", "158", "180", "201", "220", "241", "277", "306", "333", "366", "404", "447", "497", "544", "592", "662", "708", "797", "861", "954", "1020", "1131", "1226", "1352", "1456", "1600" ]
[ "nonn" ]
13
0
5
[ "A000009", "A000041", "A002865", "A007865", "A008284", "A008289", "A025065", "A085489", "A093971", "A108917", "A111133", "A236912", "A237113", "A237667", "A240861", "A275972", "A288728", "A320340", "A320347", "A323092", "A325862", "A326083", "A363225", "A363226", "A363260", "A364345", "A364346", "A364347", "A364348", "A364349" ]
null
Gus Wiseman, Jul 22 2023
2023-10-18T04:44:21
oeisdata/seq/A364/A364346.seq
ca09d739a62a0f0f8ea015ea04c516c1
A364347
Numbers k > 0 such that if prime(a) and prime(b) both divide k, then prime(a+b) does not.
[ "1", "2", "3", "4", "5", "7", "8", "9", "10", "11", "13", "14", "15", "16", "17", "19", "20", "22", "23", "25", "26", "27", "28", "29", "31", "32", "33", "34", "35", "37", "38", "39", "40", "41", "43", "44", "45", "46", "47", "49", "50", "51", "52", "53", "55", "56", "57", "58", "59", "61", "62", "64", "67", "68", "69", "71", "73", "74", "75", "76", "77", "79", "80", "81", "82", "83", "85" ]
[ "nonn" ]
15
1
2
[ "A001222", "A007865", "A056239", "A093971", "A108917", "A112798", "A236912", "A237113", "A237667", "A288728", "A299702", "A320340", "A323092", "A325862", "A326083", "A363225", "A363226", "A364345", "A364346", "A364347", "A364348", "A364350", "A364461", "A364462", "A364531" ]
null
Gus Wiseman, Jul 26 2023
2023-10-18T04:44:40
oeisdata/seq/A364/A364347.seq
3d2c51eafb18c7d7635e55b1bfebb06b
A364348
Numbers with two possibly equal divisors prime(a) and prime(b) such that prime(a+b) is also a divisor.
[ "6", "12", "18", "21", "24", "30", "36", "42", "48", "54", "60", "63", "65", "66", "70", "72", "78", "84", "90", "96", "102", "105", "108", "114", "120", "126", "130", "132", "133", "138", "140", "144", "147", "150", "154", "156", "162", "165", "168", "174", "180", "186", "189", "192", "195", "198", "204", "210", "216", "222", "228", "231", "234", "240", "246", "252" ]
[ "nonn" ]
8
1
1
[ "A001222", "A007865", "A056239", "A093971", "A108917", "A112798", "A236912", "A237113", "A237667", "A275972", "A288728", "A299702", "A320340", "A323092", "A325862", "A326083", "A363225", "A363226", "A364345", "A364346", "A364347", "A364348", "A364461", "A364462" ]
null
Gus Wiseman, Jul 27 2023
2023-10-18T04:44:56
oeisdata/seq/A364/A364348.seq
48ebc41540c78707a894007fd058c1d6
A364349
Number of strict integer partitions of n containing the sum of no subset of the parts.
[ "1", "1", "1", "2", "2", "3", "3", "5", "5", "8", "7", "11", "11", "15", "14", "21", "21", "28", "29", "38", "38", "51", "50", "65", "68", "82", "83", "108", "106", "130", "136", "163", "168", "206", "210", "248", "266", "307", "322", "381", "391", "457", "490", "553", "582", "675", "703", "797", "854", "952", "1000", "1147", "1187", "1331", "1437", "1564", "1656", "1869" ]
[ "nonn" ]
7
0
4
[ "A000009", "A000041", "A007865", "A008284", "A008289", "A025065", "A085489", "A093971", "A108917", "A111133", "A151897", "A236912", "A237113", "A237667", "A240861", "A275972", "A320340", "A320347", "A323092", "A325862", "A363226", "A364272", "A364345", "A364346", "A364349", "A364350", "A364531", "A364533", "A364534" ]
null
Gus Wiseman, Jul 29 2023
2023-07-30T09:20:19
oeisdata/seq/A364/A364349.seq
2fa8857eeca5eb5d658b2d12720ab528
A364350
Number of strict integer partitions of n such that no part can be written as a nonnegative linear combination of the others.
[ "1", "1", "1", "1", "1", "2", "1", "3", "2", "3", "3", "5", "3", "6", "5", "7", "6", "9", "7", "11", "10", "14", "12", "16", "15", "20", "17", "24", "22", "27", "29", "32", "30", "41", "36", "49", "45", "50", "52", "65", "63", "70", "77", "80", "83", "104", "98", "107", "116", "126", "134", "152", "148", "162", "180", "196", "195", "227", "227", "238", "272", "271", "293", "333", "325" ]
[ "nonn" ]
19
0
6
[ "A000009", "A000041", "A007865", "A008284", "A008289", "A085489", "A108917", "A116861", "A120641", "A151897", "A236912", "A237113", "A237667", "A275972", "A299702", "A320340", "A323092", "A326083", "A363226", "A364272", "A364350", "A364533", "A364839", "A364910", "A364911", "A364912", "A364913", "A364914", "A364915", "A364916", "A365002", "A365004", "A365006" ]
null
Gus Wiseman, Aug 15 2023
2023-09-24T04:16:25
oeisdata/seq/A364/A364350.seq
fcac6204898960b719e80ebcd3b4b0c3
A364351
Expansion of Sum_{k>0} k^2 * x^k/(1 + x^k)^3.
[ "1", "1", "15", "-6", "40", "12", "77", "-60", "180", "30", "187", "-120", "260", "56", "630", "-376", "442", "117", "551", "-340", "1218", "132", "805", "-1104", "1325", "182", "1998", "-672", "1276", "360", "1457", "-2032", "2970", "306", "3290", "-1710", "2072", "380", "4134", "-3080", "2542", "672", "2795", "-1672", "7830", "552", "3337", "-6816", "4998", "775", "7038", "-2340", "4240", "1080" ]
[ "sign" ]
16
1
3
[ "A000593", "A048272", "A309732", "A320900", "A364343", "A364351" ]
null
Seiichi Manyama, Jul 19 2023
2023-07-20T10:47:05
oeisdata/seq/A364/A364351.seq
7b47fab32c3b8630820ceb5fd6651f08
A364352
a(n) is the number of regions into which the plane is divided by n lines parallel to each edge of an equilateral triangle with side n such that the lines extend the parallel edge and divide the other edges into unit segments.
[ "7", "16", "30", "49", "73", "102", "136", "175", "219", "268", "322", "381", "445", "514", "588", "667", "751", "840", "934", "1033", "1137", "1246", "1360", "1479", "1603", "1732", "1866", "2005", "2149", "2298", "2452", "2611", "2775", "2944", "3118", "3297", "3481", "3670", "3864", "4063", "4267", "4476", "4690", "4909", "5133", "5362", "5596", "5835", "6079", "6328" ]
[ "nonn", "easy" ]
41
1
1
[ "A134238", "A147875", "A177862", "A343755", "A364352", "A364401" ]
null
Nicolay Avilov, Jul 20 2023
2023-11-24T12:21:56
oeisdata/seq/A364/A364352.seq
9eee5ab9b94a32540cd6f95b0185120e
A364353
Numbers that cannot be expressed as the sum of the squares of four Fibonacci numbers.
[ "24", "32", "40", "41", "45", "46", "48", "49", "53", "56", "57", "61", "62", "71", "80", "85", "87", "88", "92", "95", "96", "101", "103", "104", "105", "106", "108", "109", "110", "111", "112", "113", "116", "117", "119", "120", "121", "122", "124", "125", "126", "127", "131", "134", "135", "140", "142", "143", "144" ]
[ "nonn" ]
40
1
1
[ "A000045", "A007598", "A364353", "A364354" ]
null
Calvin Khor, Jul 20 2023
2023-08-24T10:41:04
oeisdata/seq/A364/A364353.seq
744afc291e8e955a1ebc98e39ba752d8
A364354
Numbers that can be expressed as the sum of the squares of four Fibonacci numbers.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "25", "26", "27", "28", "29", "30", "31", "33", "34", "35", "36", "37", "38", "39", "42", "43", "44", "47", "50", "51", "52", "54", "55", "58", "59", "60", "63", "64", "65", "66", "67", "68", "69", "70", "72", "73", "74", "75", "76", "77", "78", "79", "81", "82" ]
[ "nonn" ]
27
1
3
[ "A000045", "A007598", "A364353", "A364354" ]
null
Calvin Khor, Jul 20 2023
2023-08-21T19:38:34
oeisdata/seq/A364/A364354.seq
a61c9f757e68e397aea14725a712f4cc
A364355
Decimal expansion of the unique value of x such that Gamma(-x + i*sqrt(1-x^2)) is a real number and -1 < x < 1.
[ "5", "4", "1", "9", "7", "9", "8", "7", "1", "6", "9", "4", "8", "9", "0", "6", "0", "2", "4", "4", "3", "3", "2", "2", "7", "8", "7", "7", "9", "0", "9", "0", "4", "6", "8", "8", "0", "5", "5", "8", "2", "4", "2", "8", "0", "2", "9", "2", "7", "9", "3", "8", "4", "2", "7", "9", "5", "6", "1", "4", "5", "5", "1", "9", "4", "0", "0", "0", "0", "8", "1", "5", "8", "6", "3", "9", "1", "7", "2", "7", "4", "4", "0", "4", "6", "0", "2", "1", "5", "2", "1", "1", "5", "1", "5", "5", "5", "8", "8", "4", "8", "5", "5", "6", "6" ]
[ "nonn", "cons" ]
32
0
1
[ "A090986", "A212877", "A212878", "A212879", "A212880", "A364355", "A364356" ]
null
Artur Jasinski, Jul 20 2023
2023-08-26T15:37:32
oeisdata/seq/A364/A364355.seq
b8044d998a89f2ea40033fd3ed16f66b
A364356
Decimal expansion of negative value of function Gamma(-A364355 + i*sqrt(1-A364355^2)).
[ "6", "7", "4", "9", "3", "3", "2", "4", "7", "0", "4", "4", "9", "9", "0", "5", "9", "6", "3", "5", "3", "1", "0", "0", "4", "4", "6", "9", "5", "4", "7", "2", "2", "1", "6", "4", "2", "5", "3", "7", "4", "9", "7", "5", "6", "2", "7", "7", "8", "7", "6", "6", "1", "1", "9", "2", "8", "7", "3", "0", "3", "2", "8", "9", "4", "1", "0", "6", "4", "8", "6", "5", "9", "1", "9", "3", "3", "5", "3", "9", "9", "3", "9", "1", "4", "4", "2", "1", "3", "1", "4", "1", "5", "6", "8", "0", "9", "1", "6", "2", "0", "6", "7", "9", "7" ]
[ "nonn", "cons" ]
13
0
1
[ "A090986", "A212877", "A212878", "A212879", "A212880", "A364355", "A364356" ]
null
Artur Jasinski, Aug 08 2023
2023-08-26T15:38:11
oeisdata/seq/A364/A364356.seq
7db7c94eab6d76b5042ec42fb7214e6c
A364357
Number of divisors of n of the form 3*k+2 that are at most sqrt(n).
[ "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "2", "0", "1", "0", "1", "1", "1", "0", "1", "0", "2", "0", "1", "0", "1", "1", "1", "0", "1", "0", "2", "0", "1", "0", "1", "1", "1", "0", "1", "0", "2", "0", "1", "0", "2", "1", "1", "0", "1", "0", "2", "0", "2", "0", "1", "1", "1", "0", "1", "0", "3", "0", "1", "0", "1", "1", "1", "0", "2", "0", "2", "0", "1", "0", "1", "1", "2", "0", "1", "0", "2" ]
[ "nonn" ]
33
1
30
[ "A001822", "A038548", "A364209", "A364357" ]
null
Ilya Gutkovskiy, Jul 21 2023
2025-04-27T03:23:03
oeisdata/seq/A364/A364357.seq
33830b9398df9e25fdfffe2262490d8c
A364358
Number of divisors of n of the form 4*k+1 that are at most sqrt(n).
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "1", "1", "1", "2", "1", "1", "1", "1", "3", "1", "1", "1", "1", "2", "1", "1", "1", "2", "2" ]
[ "nonn" ]
25
1
25
[ "A001826", "A038548", "A364358", "A364387" ]
null
Ilya Gutkovskiy, Jul 21 2023
2024-12-30T01:52:34
oeisdata/seq/A364/A364358.seq
6dde85e0301a072be455eb2248d3eb7e
A364359
Primes that are the concatenation of a square and a prime that is the concatenation of two squares.
[ "419", "911", "919", "941", "1181", "1499", "1619", "1811", "4919", "8111", "9181", "9491", "9811", "11699", "12119", "12251", "14411", "14419", "16481", "16811", "19001", "22511", "22541", "32411", "32441", "36251", "44111", "44119", "44729", "49499", "49811", "52919", "57641", "64499", "64811", "67619", "72911", "81181", "90011", "90019", "91009", "92251", "94441", "97841", "98419" ]
[ "nonn", "base" ]
13
1
1
[ "A167535", "A364359" ]
null
Robert Israel, Oct 20 2023
2023-10-21T05:49:19
oeisdata/seq/A364/A364359.seq
85a9c9d60b229e9d1be49e50e66c43eb
A364360
a(n) = dpf(n) ^ tpf(n), where dpf(n) is the number of distinct prime factors of n if n >= 2 and otherwise = 0; tpf(n) is the number of all prime factors of n if n >= 2 and otherwise = 0.
[ "1", "1", "1", "1", "1", "1", "4", "1", "1", "1", "4", "1", "8", "1", "4", "4", "1", "1", "8", "1", "8", "4", "4", "1", "16", "1", "4", "1", "8", "1", "27", "1", "1", "4", "4", "4", "16", "1", "4", "4", "16", "1", "27", "1", "8", "8", "4", "1", "32", "1", "8", "4", "8", "1", "16", "4", "16", "4", "4", "1", "81", "1", "4", "8", "1", "4", "27", "1", "8", "4", "27", "1", "32", "1", "4", "8", "8", "4", "27", "1", "32", "1" ]
[ "nonn" ]
9
0
7
[ "A001221", "A001222", "A024619", "A246655", "A263653", "A363920", "A364360" ]
null
Peter Luschny, Jul 20 2023
2023-07-25T16:04:54
oeisdata/seq/A364/A364360.seq
57e32f01a2313a9768c82813724c1336
A364361
Table read by rows. T(n, k) = Sum_{j=0..n-k} k*binomial(k, j)*binomial(n - j, k).
[ "0", "0", "1", "0", "3", "2", "0", "5", "10", "3", "0", "7", "26", "21", "4", "0", "9", "50", "75", "36", "5", "0", "11", "82", "189", "164", "55", "6", "0", "13", "122", "387", "516", "305", "78", "7", "0", "15", "170", "693", "1284", "1155", "510", "105", "8", "0", "17", "226", "1131", "2724", "3405", "2262", "791", "136", "9", "0", "19", "290", "1725", "5156", "8415", "7734", "4025", "1160", "171", "10" ]
[ "nonn", "tabl" ]
8
0
5
[ "A001477", "A005408", "A014105", "A048395", "A069894", "A364361", "A364553", "A364634" ]
null
Peter Luschny, Jul 30 2023
2023-07-30T16:34:53
oeisdata/seq/A364/A364361.seq
67da2497f703784ad3e3d14a37453697
A364362
Consider all the ways to make sequences of distinct nonnegative integers using all the digits of n, such that no term has leading 0's or appears more than once in the sequence. a(n) is the minimum possible sum of any sequence of n.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "1", "11", "3", "4", "5", "6", "7", "8", "9", "10", "2", "3", "22", "5", "6", "7", "8", "9", "10", "11", "3", "4", "5", "33", "7", "8", "9", "10", "11", "12", "4", "5", "6", "7", "44", "9", "10", "11", "12", "13", "5", "6", "7", "8", "9", "55", "11", "12", "13", "14", "6", "7", "8", "9", "10", "11", "66", "13", "14", "15", "7", "8", "9", "10", "11", "12", "13" ]
[ "nonn", "base" ]
26
0
3
null
null
Thomas Richardson, Jul 20 2023
2025-01-09T19:11:30
oeisdata/seq/A364/A364362.seq
2b85f37565d95a14b2b4f18de36ab89d
A364363
a(n) is the greatest number with n prime factors, counted with multiplicity, and no decimal digit occurring more than twice, or -1 if there is no such number.
[ "1", "9988776655443322001", "9988776655443321002", "99887766554433120201", "99887766554433210201", "99887766554433221001", "99887766554433220101", "99887766554433221010", "99887766554433122010", "99887766554433220110", "99887766554433211020", "99887766554433212100", "99887766554433221100", "99887766554433200112" ]
[ "nonn", "base" ]
20
0
2
[ "A001222", "A363963", "A364363" ]
null
Zak Seidov and Robert Israel, Jul 20 2023
2023-08-02T13:48:20
oeisdata/seq/A364/A364363.seq
f05fa4af27cf0f3ad00dd1dea4b66244
A364364
For n <= 3 a(n) = n. Label a(n-3), a(n-2), a(n-1) i,j,k respectively. If i,j,k are pairwise coprime a(n) is the least unused number which shares a divisor with k. Otherwise a(n) is the least unused number coprime to j.
[ "1", "2", "3", "6", "4", "5", "7", "14", "8", "9", "11", "22", "10", "13", "17", "34", "12", "15", "19", "16", "18", "21", "23", "20", "24", "27", "25", "26", "28", "29", "31", "62", "30", "33", "37", "32", "36", "35", "41", "82", "38", "39", "43", "86", "40", "45", "47", "44", "42", "49", "53", "46", "48", "51", "55", "50", "52", "57", "59", "118", "54", "61", "65", "60", "56", "67", "69", "63" ]
[ "nonn" ]
16
1
2
[ "A091857", "A364364" ]
null
David James Sycamore, Jul 20 2023
2023-08-02T14:40:08
oeisdata/seq/A364/A364364.seq
a364f83462b4a7c5eb4a1d45bf26a41a
A364365
Start with the list of positive integers L = {1, 2, 3, ...} and set a(1) = 1. Then, for n = 1, 2, 3, ..., do the following: For each m in 1..a(n), move the number k = L(n+1) to the right by k steps. The number remaining immediately to the right of a(n) becomes a(n+1).
[ "1", "3", "6", "2", "10", "9", "5", "8", "22", "4", "13", "15", "20", "29", "7", "12", "18", "32", "59", "50", "19", "31", "14", "81", "16", "90", "17", "25", "78", "83", "21", "46", "65", "23", "41", "71", "64", "36", "53", "47", "58", "44", "35", "76", "62", "43", "88", "49", "123", "116", "27", "111", "40", "11", "69", "30", "79", "102", "24", "60", "159", "73", "248", "72", "55", "185", "45", "101", "38", "95", "141" ]
[ "nonn" ]
31
1
2
null
null
Ali Sada, Jul 20 2023
2023-08-22T23:13:57
oeisdata/seq/A364/A364365.seq
8af494340f9612faa7150057a9b5ae86
A364366
An irregular triangle read by rows, the 3rd row-symmetric Fibonaccian triangle: T(n,k) is the Whitney number of level k of the (3,n)-th symmetric Fibonaccian lattice (0 <= n, 0 <= k <= 2*n).
[ "1", "1", "1", "1", "1", "2", "2", "2", "1", "1", "3", "4", "5", "4", "3", "1", "1", "4", "7", "10", "11", "10", "7", "4", "1", "1", "5", "11", "18", "24", "26", "24", "18", "11", "5", "1", "1", "6", "16", "30", "46", "58", "63", "58", "46", "30", "16", "6", "1", "1", "7", "22", "47", "81", "116", "143", "158", "143", "116", "81", "47", "22", "7", "1" ]
[ "nonn", "tabf" ]
18
0
6
[ "A001906", "A316269", "A364366" ]
null
Robert G. Donnelly and Molly W. Dunkum, Jul 20 2023
2023-10-09T12:09:39
oeisdata/seq/A364/A364366.seq
eb298ae5e5ddeb7104a22c86c70f9534
A364367
An irregular triangle read by rows, the 4th row-symmetric Fibonaccian triangle: T(n,k) is the Whitney number of level k of the (4,n)-th symmetric Fibonaccian lattice (0 <= n, 0 <= k <= 3*n).
[ "1", "1", "1", "1", "1", "1", "2", "3", "3", "3", "2", "1", "1", "3", "6", "8", "10", "10", "8", "6", "3", "1", "1", "4", "10", "17", "25", "31", "33", "31", "25", "17", "10", "4", "1", "1", "5", "15", "31", "53", "77", "98", "110", "110", "98", "77", "53", "31", "15", "5", "1", "1", "6", "21", "51", "100", "166", "242", "313", "364", "383", "364", "313", "242", "166", "100", "51", "21", "6", "1" ]
[ "nonn", "tabf" ]
15
0
7
[ "A001353", "A316269", "A364367" ]
null
Robert G. Donnelly and Molly W. Dunkum, Jul 20 2023
2023-10-09T13:09:32
oeisdata/seq/A364/A364367.seq
af5e46fa578e148df6098cf26ef7fc09
A364368
An irregular triangle read by rows, the 5th row-symmetric Fibonaccian triangle: T(n,k) is the Whitney number of level k of the (5,n)-th symmetric Fibonaccian lattice (0 <= n, 0 <= k <= 4*n).
[ "1", "1", "1", "1", "1", "1", "1", "2", "3", "4", "4", "4", "3", "2", "1", "1", "3", "6", "10", "13", "16", "17", "16", "13", "10", "6", "3", "1", "1", "4", "10", "20", "32", "46", "59", "68", "71", "68", "59", "46", "32", "20", "10", "4", "1", "1", "5", "15", "35", "66", "109", "161", "215", "263", "296", "308", "296", "263", "215", "161", "109", "66", "35", "15", "5", "1" ]
[ "nonn", "tabf" ]
22
0
8
[ "A004254", "A316269", "A364368" ]
null
Robert G. Donnelly and Molly W. Dunkum, Jul 20 2023
2023-10-09T12:09:25
oeisdata/seq/A364/A364368.seq
a5bf6f7bbf486e49f25bf2afd005a6e6
A364369
a(n) is the least prime that is the concatenation of n squares, where the concatenations of the last k of these squares are prime for 2 <= k <= n.
[ "11", "419", "4919", "181919", "1981919", "49936919", "991981919", "9991981919", "16999369225919", "136999369225919", "99361981818199181", "1729936999369225919", "3681225936999369225919", "132481225936999369225919", "99362500576936999369225919", "8199362500576936999369225919" ]
[ "nonn", "base" ]
15
2
1
[ "A167535", "A364359", "A364369" ]
null
Robert Israel, Oct 20 2023
2023-10-22T01:25:24
oeisdata/seq/A364/A364369.seq
2e8d2622761fa8adb6602963faa91b6e
A364370
Number of chordless cycles (of length > 3) in the complement of the n-hypercube graph.
[ "0", "0", "0", "6", "160", "1720", "13056", "82656", "470016", "2496384", "12666880", "62250496", "298868736", "1409660928", "6556483584", "30148976640", "137316794368", "620328091648", "2782435737600", "12402204475392", "54971691171840", "242433274675200" ]
[ "nonn" ]
15
0
4
[ "A361149", "A364370" ]
null
Eric W. Weisstein, Jul 20 2023
2025-02-16T08:34:06
oeisdata/seq/A364/A364370.seq
84846e89edb8b3e2c613ef9a0cd698d5
A364371
G.f. satisfies A(x) = (1 + x) * (1 - x*A(x)^2).
[ "1", "0", "-1", "2", "-2", "-1", "9", "-20", "20", "24", "-150", "327", "-293", "-599", "3097", "-6452", "4854", "15878", "-71252", "140112", "-81328", "-437346", "1746254", "-3214989", "1223971", "12345295", "-44552833", "76242173", "-11292089", "-354175849", "1167638037", "-1842585992", "-233903034", "10273377388", "-31169512310" ]
[ "sign", "easy" ]
18
0
4
[ "A000108", "A073157", "A364371", "A364372", "A364373", "A364375" ]
null
Seiichi Manyama, Jul 20 2023
2024-08-28T02:34:28
oeisdata/seq/A364/A364371.seq
f124baa16be0e9eeb1e14ee95ab07aa9
A364372
G.f. satisfies A(x) = (1 + x) * (1 - x*A(x)^3).
[ "1", "0", "-1", "3", "-6", "6", "15", "-107", "349", "-672", "39", "5835", "-27654", "75765", "-95799", "-279129", "2297970", "-8377854", "17663640", "-996624", "-177445221", "888491025", "-2551959604", "3337931168", "10407149226", "-87719805853", "328682535695", "-708428979213", "15252552804", "7616368090377", "-38693979668535" ]
[ "sign", "easy" ]
17
0
4
[ "A364336", "A364371", "A364372", "A364373", "A364376" ]
null
Seiichi Manyama, Jul 20 2023
2024-09-09T09:35:24
oeisdata/seq/A364/A364372.seq
869816b88ea012a5270770fff3f5b3df
A364373
G.f. satisfies A(x) = (1 + x) * (1 - x*A(x)^4).
[ "1", "0", "-1", "4", "-12", "26", "-14", "-236", "1604", "-6577", "17827", "-14064", "-186496", "1437856", "-6416576", "18733256", "-17358808", "-201270728", "1652571996", "-7692333934", "23375782030", "-23913813710", "-250917362258", "2147925544190", "-10270145045142", "32053993413694", "-35259817590134" ]
[ "sign" ]
9
0
4
[ "A364337", "A364371", "A364372", "A364373" ]
null
Seiichi Manyama, Jul 20 2023
2023-07-21T11:09:48
oeisdata/seq/A364/A364373.seq
c869db2b442ff95c307a0d16a75935a7
A364374
G.f. satisfies A(x) = (1 + x*A(x)) * (1 - x*A(x)^2).
[ "1", "0", "-1", "1", "2", "-6", "-1", "28", "-31", "-98", "288", "131", "-1730", "1638", "7431", "-19583", "-15502", "135642", "-99523", "-664050", "1535896", "1816196", "-11902728", "5944326", "64487669", "-129346490", "-213116764", "1112382523", "-277762230", "-6572175490", "11287106695", "25078981772", "-107983368519", "-1826241850" ]
[ "sign", "easy" ]
26
0
5
[ "A007863", "A057078", "A364371", "A364374", "A364375", "A364376" ]
null
Seiichi Manyama, Jul 21 2023
2024-09-08T08:25:09
oeisdata/seq/A364/A364374.seq
899505c191bef486830d62003bf9b40f
A364375
G.f. satisfies A(x) = (1 + x*A(x)) * (1 - x*A(x)^3).
[ "1", "0", "-1", "2", "0", "-11", "28", "1", "-206", "564", "38", "-4711", "13329", "1273", "-119762", "344707", "41884", "-3251250", "9445976", "1381154", "-92305098", "269504686", "45848871", "-2707126108", "7921304973", "1532928960", "-81375728566", "238196143730", "51591751698", "-2493907008116", "7293147604136" ]
[ "sign", "easy" ]
17
0
4
[ "A198953", "A364371", "A364372", "A364374", "A364375", "A364376" ]
null
Seiichi Manyama, Jul 21 2023
2024-08-27T09:19:30
oeisdata/seq/A364/A364375.seq
82374f5048bf6fbcf07266afb589d6ac
A364376
G.f. satisfies A(x) = (1 + x*A(x)) * (1 - x*A(x)^4).
[ "1", "0", "-1", "3", "-4", "-9", "73", "-212", "111", "1956", "-10078", "21466", "29823", "-418183", "1561911", "-1722963", "-13205004", "86962328", "-232448945", "-109578204", "3849218852", "-17135183489", "27800381006", "113891855632", "-966644138742", "3075070731677", "-833503324311", "-41673632701038" ]
[ "sign", "easy" ]
15
0
4
[ "A215623", "A364372", "A364374", "A364375", "A364376" ]
null
Seiichi Manyama, Jul 21 2023
2024-09-09T09:35:28
oeisdata/seq/A364/A364376.seq
92ce7d4abcbf22665bca82e7efe59208
A364377
The number of trailing 0's in the representation of n in Jacobsthal greedy base (A265747).
[ "0", "0", "1", "0", "2", "0", "0", "1", "0", "2", "3", "0", "0", "1", "0", "2", "0", "0", "1", "0", "4", "0", "0", "1", "0", "2", "0", "0", "1", "0", "2", "3", "0", "0", "1", "0", "2", "0", "0", "1", "0", "4", "5", "0", "0", "1", "0", "2", "0", "0", "1", "0", "2", "3", "0", "0", "1", "0", "2", "0", "0", "1", "0", "4", "0", "0", "1", "0", "2", "0", "0", "1", "0", "2", "3", "0", "0", "1", "0", "2", "0", "0", "1", "0", "6", "0", "0" ]
[ "nonn", "base" ]
9
1
5
[ "A001045", "A265747", "A324477", "A364377" ]
null
Amiram Eldar, Jul 21 2023
2023-07-29T03:22:14
oeisdata/seq/A364/A364377.seq
7e2909f732baa6d8456de23af8d2b716
A364378
Numbers whose representation in Jacobsthal greedy base (A265747) is palindromic.
[ "0", "1", "2", "4", "6", "9", "12", "20", "22", "27", "36", "41", "44", "60", "68", "84", "86", "97", "112", "123", "132", "143", "158", "169", "172", "204", "220", "252", "260", "292", "308", "340", "342", "363", "396", "417", "432", "453", "486", "507", "516", "537", "570", "591", "606", "627", "660", "681", "684", "748", "780", "844", "860", "924", "956", "1020", "1028" ]
[ "nonn", "base" ]
8
1
3
[ "A001045", "A002113", "A006995", "A014190", "A014825", "A084639", "A094202", "A128209", "A265747", "A331191", "A351712", "A351717", "A352087", "A352105", "A352319", "A352341", "A364214", "A364378" ]
null
Amiram Eldar, Jul 21 2023
2023-07-29T03:21:55
oeisdata/seq/A364/A364378.seq
4e00deddb4bab745e67a6a048f5d0996
A364379
Greedy Jacobsthal-Niven numbers: numbers that are divisible by the sum of the digits in their representation in Jacobsthal greedy base (A265747).
[ "1", "2", "3", "4", "5", "6", "8", "9", "10", "11", "12", "14", "15", "16", "20", "21", "22", "24", "26", "27", "28", "32", "33", "36", "40", "42", "43", "44", "45", "46", "48", "51", "52", "54", "56", "57", "60", "64", "68", "69", "72", "75", "76", "80", "84", "85", "86", "87", "88", "90", "92", "93", "96", "99", "100", "104", "105", "106", "108", "111", "112", "115", "116", "117", "120" ]
[ "nonn", "base" ]
10
1
2
[ "A005349", "A049445", "A064150", "A064438", "A064481", "A118363", "A265745", "A265747", "A328208", "A328212", "A331085", "A331728", "A333426", "A334308", "A342426", "A342726", "A344341", "A351714", "A351719", "A352089", "A352107", "A352320", "A352342", "A352508", "A364216", "A364379", "A364380", "A364381", "A364382", "A364383" ]
null
Amiram Eldar, Jul 21 2023
2023-07-29T03:21:34
oeisdata/seq/A364/A364379.seq
3a1d1c0986ff411918ed159d03afe3b4
A364380
Numbers k such that k and k+1 are both greedy Jacobsthal-Niven numbers (A364379).
[ "1", "2", "3", "4", "5", "8", "9", "10", "11", "14", "15", "20", "21", "26", "27", "32", "42", "43", "44", "45", "51", "56", "68", "75", "84", "85", "86", "87", "92", "99", "104", "105", "111", "115", "116", "125", "128", "135", "144", "155", "170", "171", "176", "182", "183", "195", "204", "213", "219", "224", "260", "264", "267", "275", "304", "305", "324", "329", "341", "344" ]
[ "nonn", "base" ]
8
1
2
[ "A265745", "A265747", "A328205", "A328209", "A328213", "A330927", "A330931", "A331086", "A331820", "A333427", "A334309", "A342427", "A344342", "A351715", "A351720", "A352090", "A352108", "A352321", "A352343", "A352509", "A364217", "A364379", "A364380", "A364381", "A364382", "A364383" ]
null
Amiram Eldar, Jul 21 2023
2023-07-29T03:21:11
oeisdata/seq/A364/A364380.seq
cdcce2c7f68b8fe5f2c31a26b89a40a3
A364381
Starts of runs of 3 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).
[ "1", "2", "3", "4", "8", "9", "10", "14", "20", "26", "42", "43", "44", "84", "85", "86", "104", "115", "170", "182", "304", "344", "362", "414", "544", "682", "686", "692", "784", "854", "1014", "1370", "1384", "1504", "1673", "1685", "1706", "2224", "2315", "2358", "2730", "2731", "2732", "2763", "2774", "3243", "3594", "3702", "4144", "4688", "4864", "5046", "5408" ]
[ "nonn", "base" ]
9
1
2
[ "A154701", "A265745", "A265747", "A328206", "A328210", "A328214", "A330932", "A331087", "A331822", "A333428", "A334310", "A342428", "A344343", "A351716", "A351721", "A352091", "A352109", "A352322", "A352344", "A352510", "A364218", "A364379", "A364380", "A364381", "A364382", "A364383" ]
null
Amiram Eldar, Jul 21 2023
2023-07-29T03:20:30
oeisdata/seq/A364/A364381.seq
5dce7f1e7a63f20c81e01e9828d2d40a
A364382
Starts of runs of 4 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).
[ "1", "2", "3", "8", "9", "42", "43", "84", "85", "2730", "2731", "5460", "5461", "21864", "21865", "59477", "60073", "66303", "75048", "112509", "156607", "174762", "174763", "283327", "312190", "320768", "349524", "349525", "351570", "354429", "374589", "384039", "479037", "504510", "527103", "624040", "625470", "656829", "688830", "711423" ]
[ "nonn", "base" ]
8
1
2
[ "A141769", "A265745", "A265747", "A328207", "A328211", "A328215", "A330933", "A331824", "A334311", "A342429", "A344344", "A352092", "A352110", "A352345", "A352511", "A364219", "A364379", "A364380", "A364381", "A364382", "A364383" ]
null
Amiram Eldar, Jul 21 2023
2023-07-29T03:20:13
oeisdata/seq/A364/A364382.seq
c87376b811e0ee57013a897298a1eaf9
A364383
Starts of runs of 5 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).
[ "1", "2", "8", "42", "84", "2730", "5460", "21864", "174762", "349524", "8575060", "11184810", "89478504", "106502227", "109295017", "181276927", "181843540", "184069717", "223830100", "245705471", "279956051", "280652201", "287571966", "291006547", "316295081", "316991231", "358660180", "360195667", "362988457", "422527571" ]
[ "nonn", "base" ]
7
1
2
[ "A265745", "A265747", "A330928", "A364220", "A364379", "A364380", "A364381", "A364382", "A364383" ]
null
Amiram Eldar, Jul 21 2023
2023-07-29T03:19:08
oeisdata/seq/A364/A364383.seq
369a3ff0101e8e1ee362133d36dafcfe
A364384
a(n) is the number of quadratic equations u*x^2 + v*x + w = 0 with different solution sets L != {}, where n = abs(u) + abs(v) + abs(w), the coefficients u, v, w as well as the solutions x_1, x_2 are integers and GCD(u, v, w) = 1.
[ "1", "3", "2", "6", "3", "6", "2", "8", "4", "7", "4", "8", "2", "10", "4", "8", "5", "10", "2", "10", "4", "10", "4", "10", "4", "11", "6", "8", "4", "12", "2", "14", "4", "8", "6", "12", "5", "12", "4", "10", "4", "14", "2", "14", "6", "8", "6", "12", "4", "15", "6", "10", "4", "12", "4", "14", "6", "12", "4", "14", "2", "14", "6", "10", "9", "14", "4", "12", "4", "12", "4", "18", "2", "16", "6", "8", "8", "12", "4", "16", "6", "13", "6", "14", "4", "14", "6", "10", "4", "18", "4", "18", "6", "8", "6", "14", "4", "16", "6", "14" ]
[ "easy", "nonn" ]
24
1
2
[ "A364384", "A364385", "A365876", "A365877", "A365892" ]
null
Felix Huber, Jul 22 2023
2023-10-05T14:20:24
oeisdata/seq/A364/A364384.seq
a87925ed095ced7f61834136a043844f
A364385
a(n) is the number of quadratic equations u*x^2 + v*x + w = 0 with different solution sets L != {}, where n >= abs(u) + abs(v) + abs(w) and the coefficients u, v, w as well as the solutions x_1, x_2 are integers.
[ "1", "4", "6", "12", "15", "21", "23", "31", "35", "42", "46", "54", "56", "66", "70", "78", "83", "93", "95", "105", "109", "119", "123", "133", "137", "148", "154", "162", "166", "178", "180", "194", "198", "206", "212", "224", "229", "241", "245", "255", "259", "273", "275", "289", "295", "303", "309", "321", "325", "340", "346", "356", "360", "372", "376", "390", "396" ]
[ "easy", "nonn" ]
31
1
2
[ "A364384", "A364385", "A365876", "A365877", "A365892" ]
null
Felix Huber, Jul 22 2023
2024-12-29T15:02:53
oeisdata/seq/A364/A364385.seq
0da8ce253e157dff1f0686d12d901d65
A364386
Triangle T(n,k) read by rows: the number of Motzkin paths of length n that have k nodes at their peak level, 1 <= k <= n+1.
[ "1", "0", "1", "1", "0", "1", "2", "1", "0", "1", "4", "3", "1", "0", "1", "8", "7", "4", "1", "0", "1", "18", "15", "11", "5", "1", "0", "1", "44", "33", "26", "16", "6", "1", "0", "1", "113", "78", "59", "42", "22", "7", "1", "0", "1", "296", "197", "138", "101", "64", "29", "8", "1", "0", "1", "782", "518", "342", "240", "165", "93", "37", "9", "1", "0", "1", "2076", "1388", "892", "590", "406", "258", "130", "46", "10", "1", "0", "1" ]
[ "nonn", "tabl" ]
18
0
7
[ "A001006", "A088457", "A152879", "A364386" ]
null
R. J. Mathar, Jul 21 2023
2024-04-16T18:00:53
oeisdata/seq/A364/A364386.seq
7f95887870de60b3dcc0dafb496ec52a
A364387
Number of divisors of n of the form 4*k+3 that are at most sqrt(n).
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "0", "2", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "0", "2", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "1", "1" ]
[ "nonn" ]
12
1
63
[ "A001842", "A038548", "A364358", "A364387" ]
null
Ilya Gutkovskiy, Jul 21 2023
2024-12-29T22:31:21
oeisdata/seq/A364/A364387.seq
bc5ced7601abac50fe7f5161250a391d
A364388
Number of divisors of n of the form 5*k+1 that are at most sqrt(n).
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1" ]
[ "nonn" ]
6
1
36
[ "A001876", "A038548", "A364388", "A364389" ]
null
Ilya Gutkovskiy, Jul 21 2023
2023-07-23T13:42:31
oeisdata/seq/A364/A364388.seq
4bee3e4533ace68298386e728d6134a7
A364389
Number of divisors of n of the form 5*k+2 that are at most sqrt(n).
[ "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "2", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "2", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "2", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "2", "0", "1" ]
[ "nonn" ]
5
1
56
[ "A001877", "A038548", "A364388", "A364389" ]
null
Ilya Gutkovskiy, Jul 21 2023
2023-07-23T13:42:22
oeisdata/seq/A364/A364389.seq
4d20ec06fb91b07ed5dc204e7e875586
A364390
Triangle T(n, k) based on A176040 which read by rows yields a permutation of the positive integers.
[ "1", "3", "2", "8", "7", "4", "10", "9", "6", "5", "19", "18", "15", "14", "11", "21", "20", "17", "16", "13", "12", "34", "33", "30", "29", "26", "25", "22", "36", "35", "32", "31", "28", "27", "24", "23", "53", "52", "49", "48", "45", "44", "41", "40", "37", "55", "54", "51", "50", "47", "46", "43", "42", "39", "38", "76", "75", "72", "71", "68", "67", "64", "63", "60", "59", "56", "78", "77", "74", "73", "70", "69", "66", "65", "62", "61", "58", "57" ]
[ "nonn", "easy", "tabl" ]
12
1
2
[ "A000217", "A006003", "A176040", "A364390" ]
null
Werner Schulte, Jul 21 2023
2023-12-04T06:32:10
oeisdata/seq/A364/A364390.seq
0baf41a1fa0b4ffb7c9bfd2e74cf829c
A364391
a(n) = n - (largest nontrivial divisor of n, or 0 if there is none).
[ "1", "2", "3", "2", "5", "3", "7", "4", "6", "5", "11", "6", "13", "7", "10", "8", "17", "9", "19", "10", "14", "11", "23", "12", "20", "13", "18", "14", "29", "15", "31", "16", "22", "17", "28", "18", "37", "19", "26", "20", "41", "21", "43", "22", "30", "23", "47", "24", "42", "25", "34", "26", "53", "27", "44", "28", "38", "29", "59", "30", "61", "31", "42", "32", "52", "33", "67", "34", "46", "35" ]
[ "nonn" ]
17
1
2
[ "A032742", "A060681", "A364391" ]
null
Todor Szimeonov, Jul 21 2023
2023-08-21T08:25:27
oeisdata/seq/A364/A364391.seq
53b068e7677322e0fca5f11806b89d13
A364392
a(1)=1 and thereafter a(n) is the least number of locations 1..n-1 which can be visited in a single path beginning at i=n-1, in which one proceeds from location i to i +- a(i) (within 1..n-1) until no further unvisited location is available.
[ "1", "1", "2", "3", "4", "4", "3", "6", "3", "4", "4", "6", "3", "5", "4", "7", "5", "5", "6", "6", "5", "6", "6", "6", "6", "7", "3", "8", "5", "8", "7", "5", "6", "6", "7", "7", "9", "5", "9", "7", "5", "8", "7", "8", "3", "6", "9", "9", "7", "6", "4", "6", "6", "6", "10", "7", "7", "5", "10", "3", "6", "7", "7", "8", "3", "8", "6", "5", "9", "6", "4", "9", "9", "5", "7", "6", "5", "5", "7", "5", "6", "6", "6", "7", "7", "9", "7" ]
[ "nonn", "easy" ]
40
1
3
[ "A360593", "A360745", "A360746", "A364392", "A364882" ]
null
Neal Gersh Tolunsky, Jul 21 2023
2024-12-19T11:46:19
oeisdata/seq/A364/A364392.seq
fbb88c16b678b8a09d3c11549beb13c7
A364393
G.f. satisfies A(x) = 1 + x*(1 + 1/A(x)^2).
[ "1", "2", "-4", "20", "-120", "800", "-5696", "42416", "-326304", "2572992", "-20685696", "168920704", "-1397257472", "11682707712", "-98578346496", "838369268480", "-7178912946688", "61842549386240", "-535575159363584", "4660216874719232", "-40722264390799360", "357204260381327360" ]
[ "sign" ]
24
0
2
[ "A346626", "A364393", "A364395", "A364397", "A364399" ]
null
Seiichi Manyama, Jul 22 2023
2023-10-21T11:10:12
oeisdata/seq/A364/A364393.seq
df447440e565d74ccb2edb2801d0fba6
A364394
G.f. satisfies A(x) = 1 + x/A(x)*(1 + 1/A(x)).
[ "1", "2", "-6", "34", "-238", "1858", "-15510", "135490", "-1223134", "11320066", "-106830502", "1024144482", "-9945711566", "97634828354", "-967298498358", "9659274283650", "-97119829841854", "982391779220482", "-9990160542904134", "102074758837531810", "-1047391288012377774", "10788532748880319298" ]
[ "sign" ]
30
0
2
[ "A027307", "A087197", "A108424", "A112478", "A364394", "A364396", "A364398" ]
null
Seiichi Manyama, Jul 22 2023
2023-10-21T11:09:47
oeisdata/seq/A364/A364394.seq
5ec0c89c19a3a9d7134c84f9a9971ab1
A364395
G.f. satisfies A(x) = 1 + x/A(x)*(1 + 1/A(x)^2).
[ "1", "2", "-8", "60", "-552", "5648", "-61712", "705104", "-8321696", "100658368", "-1241281536", "15546987648", "-197234640384", "2529169695232", "-32728878054144", "426864306146560", "-5605439340018176", "74050470138645504", "-983432207024885760", "13122261492710033408", "-175836387068096147456" ]
[ "sign" ]
26
0
2
[ "A219534", "A364393", "A364395", "A364397", "A364399" ]
null
Seiichi Manyama, Jul 22 2023
2024-03-03T10:32:45
oeisdata/seq/A364/A364395.seq
3f132566f472aa73f4c572735709251e
A364396
G.f. satisfies A(x) = 1 + x/A(x)^2*(1 + 1/A(x)).
[ "1", "2", "-10", "86", "-902", "10506", "-130594", "1697006", "-22774094", "313205522", "-4391039930", "62522730310", "-901680559574", "13143551082138", "-193339856081490", "2866341942620382", "-42784807130635678", "642457682754511906", "-9698259831536382826", "147091417979841002294" ]
[ "sign" ]
16
0
2
[ "A112478", "A144097", "A364394", "A364396", "A364398" ]
null
Seiichi Manyama, Jul 22 2023
2023-10-21T06:12:49
oeisdata/seq/A364/A364396.seq
71b463612d108a82aa93353fc396974d
A364397
G.f. satisfies A(x) = 1 + x/A(x)^2*(1 + 1/A(x)^2).
[ "1", "2", "-12", "124", "-1560", "21776", "-324256", "5046096", "-81086112", "1335113408", "-22408067200", "381942129792", "-6593494698752", "115044039049728", "-2025580621035520", "35943759448886528", "-642162301086308864", "11541259115333684224", "-208521418711421405184" ]
[ "sign" ]
19
0
2
[ "A363311", "A364393", "A364395", "A364397", "A364399" ]
null
Seiichi Manyama, Jul 22 2023
2023-10-21T11:07:13
oeisdata/seq/A364/A364397.seq
e6d37830aaee2827ea5c976e43d179d4
A364398
G.f. satisfies A(x) = 1 + x/A(x)^3*(1 + 1/A(x)).
[ "1", "2", "-14", "162", "-2270", "35234", "-582958", "10076354", "-179802046", "3287029698", "-61246957902", "1158889656930", "-22207636788894", "430106644358242", "-8405699952109166", "165557885912786818", "-3282954949273886590", "65487784219460233602", "-1313225110482709157518" ]
[ "sign" ]
30
0
2
[ "A112478", "A260332", "A364394", "A364396", "A364398", "A364399", "A364400" ]
null
Seiichi Manyama, Jul 22 2023
2023-10-21T11:08:52
oeisdata/seq/A364/A364398.seq
28b05e75f335729acbe9d1a091830759
A364399
G.f. satisfies A(x) = 1 + x/A(x)^3*(1 + 1/A(x)^2).
[ "1", "2", "-16", "212", "-3400", "60384", "-1142960", "22598832", "-461250208", "9644611008", "-205537131008", "4447969973888", "-97482797466624", "2159242220999936", "-48260706692535552", "1087076798266594048", "-24652590023639251456", "562396337623786449920" ]
[ "sign" ]
19
0
2
[ "A363380", "A364393", "A364395", "A364397", "A364398", "A364399", "A364400" ]
null
Seiichi Manyama, Jul 22 2023
2023-10-21T11:08:16
oeisdata/seq/A364/A364399.seq
8c77c3d05bb34290e13fd123beb93e0a
A364400
G.f. satisfies A(x) = 1 + x/A(x)^3*(1 + 1/A(x)^3).
[ "1", "2", "-18", "270", "-4902", "98538", "-2110794", "47227846", "-1090742094", "25806364434", "-622267199554", "15236456140542", "-377814588773622", "9468373002766074", "-239434464005544570", "6101951612867546166", "-156561081975745809566", "4040863076496835880226" ]
[ "sign" ]
16
0
2
[ "A363304", "A364398", "A364399", "A364400" ]
null
Seiichi Manyama, Jul 22 2023
2023-10-21T11:07:49
oeisdata/seq/A364/A364400.seq
8e4c35a1c54908815869bd7fe6aa8b12