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1999-12-11 03:00:00
2025-04-28 00:58:08
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A379502
Characteristic function of almost Zumkeller numbers: a(n) = 1 if Zumkeller-deficiency of n (A103977) is 1, otherwise 0.
[ "1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "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", "1", "0", "0", "0", "0", "0", "0", "0", "1", "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", "1", "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", "1" ]
[ "nonn" ]
13
1
null
[ "A083207", "A103977", "A379502", "A379503", "A379504" ]
null
Antti Karttunen, Jan 06 2025
2025-01-07T08:47:04
oeisdata/seq/A379/A379502.seq
c577a1981f9ee4cf05594b26c8efeaed
A379503
Almost Zumkeller numbers: Numbers whose Zumkeller-deficiency (A103977) is 1.
[ "1", "2", "4", "8", "16", "18", "32", "36", "64", "72", "100", "128", "144", "162", "196", "200", "256", "288", "324", "392", "400", "450", "512", "576", "648", "784", "800", "882", "900", "968", "1024", "1152", "1296", "1352", "1458", "1568", "1600", "1764", "1800", "1936", "2048", "2178", "2304", "2450", "2500", "2592", "2704", "2916", "3042", "3136", "3200", "3528", "3600", "3872", "4050", "4096", "4356", "4608", "4624", "4900", "5000" ]
[ "nonn" ]
38
1
2
[ "A000079", "A028982", "A083207", "A083210", "A103977", "A156942", "A379502", "A379503", "A379504" ]
null
Antti Karttunen, Jan 06 2025
2025-01-07T08:47:43
oeisdata/seq/A379/A379503.seq
7ea772b3a55182832fdc0ec0b54b1a24
A379504
a(n) is the number of ways of partitioning the divisors of n into two disjoint sets with equal sum, when an extra 1-divisor is added to the divisor set, and the two 1-divisors are considered distinct from each other.
[ "1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "8", "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", "1", "0", "0", "0", "0", "0", "0", "0", "26", "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", "2", "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", "1" ]
[ "nonn" ]
34
1
18
[ "A000079", "A083206", "A103977", "A156942", "A379502", "A379503", "A379504", "A379505" ]
null
Antti Karttunen, Jan 06 2025
2025-01-07T15:56:05
oeisdata/seq/A379/A379504.seq
a7e93248420503f2609ee7feb06b8502
A379505
a(n) is the number of ways of partitioning the divisors of n into two disjoint sets with equal sum, when an extra 1-divisor is added to the divisor set, and the two 1-divisors are considered indistinguishable.
[ "1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "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", "1", "0", "0", "0", "0", "0", "0", "0", "21", "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", "2", "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", "1" ]
[ "nonn" ]
18
1
18
[ "A000079", "A083206", "A103977", "A156942", "A336700", "A379502", "A379503", "A379504", "A379505" ]
null
Antti Karttunen, Jan 07 2025
2025-01-07T15:56:10
oeisdata/seq/A379/A379505.seq
9d9fb4ef9d6bec13303b622f39deeff4
A379506
Sequence of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its inradius the semiperimeter of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers.
[ "3", "4", "5", "13", "84", "85", "183", "16744", "16745", "33673", "566935464", "566935465", "1133904603", "642869824352293804", "642869824352293805", "1285739649838492213", "826563223583404284483387832630818684", "826563223583404284483387832630818685" ]
[ "nonn", "tabf" ]
9
1
1
[ "A002065", "A365577", "A365578", "A365796", "A378395", "A378963", "A379506" ]
null
Miguel-Ángel Pérez García-Ortega, Dec 23 2024
2025-01-17T17:07:54
oeisdata/seq/A379/A379506.seq
38a1f95a9ee10ba81a465924f330cbaa
A379507
For n >= 1, a(n) = GCD((2*n)! / (n!)^2, 105).
[ "1", "3", "5", "35", "21", "21", "3", "15", "5", "1", "21", "7", "35", "15", "15", "15", "15", "105", "105", "105", "15", "15", "15", "15", "21", "21", "7", "35", "105", "7", "7", "21", "105", "105", "21", "7", "7", "105", "35", "35", "105", "105", "105", "105", "105", "105", "105", "105", "15", "3", "3", "3", "105", "105", "21", "3", "3", "15", "15", "21", "21", "21", "15", "15", "15", "15" ]
[ "nonn" ]
11
1
2
[ "A000142", "A000984", "A379507" ]
null
Ctibor O. Zizka, Dec 23 2024
2024-12-23T22:05:18
oeisdata/seq/A379/A379507.seq
c3ef60d84528dbd4ed4aba8059a1855f
A379508
Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
[ "1", "97", "3361", "114241", "3880897", "131836321", "4478554081", "152139002497", "5168247530881", "175568277047521", "5964153172084897", "202605639573839041", "6882627592338442561", "233806732499933208097", "7942546277405390632801", "269812766699283348307201", "9165691521498228451812097", "311363698964240484013304161" ]
[ "nonn", "easy" ]
9
0
2
[ "A002315", "A377011", "A377016", "A377017", "A377726", "A378965", "A379508" ]
null
Miguel-Ángel Pérez García-Ortega, Dec 23 2024
2025-01-17T17:08:45
oeisdata/seq/A379/A379508.seq
17bd6b260a9b4fbfd4ee4dd657bcc71e
A379509
Sum of the legs of the unique primitive Pythagorean triple whose inradius is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
[ "7", "127", "3527", "115199", "3886471", "131868799", "4478743367", "152140105727", "5168253960967", "175568314524799", "5964153390518471", "202605640846963199", "6882627599758753927", "233806732543181952127", "7942546277657462785607", "269812766700752532479999", "9165691521506791484696071", "311363698964290393026435199" ]
[ "nonn", "easy" ]
8
0
1
[ "A002315", "A377025", "A378380", "A378386", "A379509" ]
null
Miguel-Ángel Pérez García-Ortega, Dec 23 2024
2025-01-17T17:05:58
oeisdata/seq/A379/A379509.seq
81e27e276a31d3e0d5362cb1ff738634
A379510
a(n) = n + floor(n*r/t) + floor(n*s/t), where r=2^(1/4), s=2^(1/2), t=2^(3/4).
[ "1", "4", "7", "9", "12", "15", "16", "19", "22", "25", "27", "30", "32", "34", "37", "40", "43", "45", "47", "50", "52", "55", "58", "60", "63", "65", "68", "70", "73", "76", "78", "80", "83", "86", "88", "91", "94", "95", "98", "101", "103", "106", "109", "111", "113", "116", "119", "121", "124", "127", "129", "131", "134", "137", "139", "142", "144", "147", "149", "152" ]
[ "nonn" ]
11
1
2
[ "A000027", "A184812", "A378142", "A378185", "A379510" ]
null
Clark Kimberling, Jan 13 2025
2025-01-13T20:30:13
oeisdata/seq/A379/A379510.seq
1ffa82cb9c5401f5b4d9777288559254
A379511
a(n) = floor(n*(2^(1/4) + 2^(-1/4))); Beatty sequence for 2^(1/4) + 2^(-1/4).
[ "2", "4", "6", "8", "10", "12", "14", "16", "18", "20", "22", "24", "26", "28", "30", "32", "34", "36", "38", "40", "42", "44", "46", "48", "50", "52", "54", "56", "58", "60", "62", "64", "66", "69", "71", "73", "75", "77", "79", "81", "83", "85", "87", "89", "91", "93", "95", "97", "99", "101", "103", "105", "107", "109", "111", "113", "115", "117", "119", "121", "123", "125" ]
[ "nonn" ]
15
1
1
[ "A378142", "A379511" ]
null
Clark Kimberling, Jan 11 2025
2025-01-23T00:02:58
oeisdata/seq/A379/A379511.seq
72e3dd44605ef2b57b96334706988645
A379512
Erase digits 0 and 1 from decimal expansion of n. Then keep just the coprime digits; write 0 if all digits disappear.
[ "0", "0", "2", "3", "4", "5", "6", "7", "8", "9", "0", "0", "2", "3", "4", "5", "6", "7", "8", "9", "2", "2", "0", "23", "0", "25", "0", "27", "0", "29", "3", "3", "32", "0", "34", "35", "0", "37", "38", "0", "4", "4", "0", "43", "0", "45", "0", "47", "0", "49", "5", "5", "52", "53", "54", "0", "56", "57", "58", "59", "6", "6", "0", "0", "0", "65", "0", "67", "0", "0", "7", "7", "72", "73", "74", "75", "76", "0", "78", "79", "8", "8", "0", "83", "0", "85", "0", "87" ]
[ "nonn", "base", "easy" ]
49
0
3
[ "A004151", "A004719", "A059717", "A379512" ]
null
Ctibor O. Zizka, Jan 21 2025
2025-01-21T10:54:50
oeisdata/seq/A379/A379512.seq
1819e4446945054d0a80a636b92338af
A379513
Numerators of the partial sums of the reciprocals of the sum of unitary divisors function (A034448).
[ "1", "4", "19", "107", "39", "61", "259", "817", "853", "97", "301", "307", "2209", "187", "2279", "39583", "121129", "122557", "124699", "126127", "509863", "171541", "173921", "526523", "6930479", "6983519", "7063079", "7118771", "7193027", "802663", "405199", "13495327", "1131701", "30726097", "123670153", "622026437", "11910394103" ]
[ "nonn", "easy", "frac" ]
9
1
2
[ "A001620", "A034448", "A064609", "A308041", "A370898", "A379513", "A379514", "A379515" ]
null
Amiram Eldar, Dec 23 2024
2024-12-24T07:29:28
oeisdata/seq/A379/A379513.seq
730dbfef6a076150f5fb5e9e5f8cde50
A379514
Denominators of the partial sums of the reciprocals of the sum of unitary divisors function (A034448).
[ "1", "3", "12", "60", "20", "30", "120", "360", "360", "40", "120", "120", "840", "70", "840", "14280", "42840", "42840", "42840", "42840", "171360", "57120", "57120", "171360", "2227680", "2227680", "2227680", "2227680", "2227680", "247520", "123760", "4084080", "340340", "9189180", "36756720", "183783600", "3491888400", "3491888400" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A034448", "A064609", "A370898", "A379513", "A379514", "A379516" ]
null
Amiram Eldar, Dec 23 2024
2024-12-24T07:28:42
oeisdata/seq/A379/A379514.seq
afdc2111b96b94c122618a4e5d37e493
A379515
Numerators of the partial alternating sums of the reciprocals of the sum of unitary divisors function (A034448).
[ "1", "2", "11", "43", "53", "4", "37", "293", "329", "103", "113", "107", "809", "129", "809", "12913", "41119", "39691", "41833", "8081", "33395", "32443", "33871", "10973", "148361", "48275", "7149", "34861", "108119", "319937", "164941", "1761311", "112361", "662011", "5405483", "26502319", "516671461", "508357441", "3620857237", "3556192637" ]
[ "nonn", "easy", "frac" ]
8
1
2
[ "A034448", "A064609", "A308041", "A323482", "A370898", "A379513", "A379515", "A379516" ]
null
Amiram Eldar, Dec 23 2024
2024-12-24T07:28:24
oeisdata/seq/A379/A379515.seq
1316e84df03160eb64460d547cb21a82
A379516
Denominators of the partial alternating sums of the reciprocals of the sum of unitary divisors function (A034448).
[ "1", "3", "12", "60", "60", "5", "40", "360", "360", "120", "120", "120", "840", "140", "840", "14280", "42840", "42840", "42840", "8568", "34272", "34272", "34272", "11424", "148512", "49504", "7072", "35360", "106080", "318240", "159120", "1750320", "109395", "656370", "5250960", "26254800", "498841200", "498841200", "3491888400", "3491888400" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A034448", "A064609", "A370898", "A379514", "A379515", "A379516" ]
null
Amiram Eldar, Dec 23 2024
2024-12-24T07:27:44
oeisdata/seq/A379/A379516.seq
7bcc6a36ede2520ce24b5523f8676543
A379517
Numerators of the partial sums of the reciprocals of the unitary totient function (A047994).
[ "1", "2", "5", "17", "37", "43", "15", "109", "225", "239", "1223", "3809", "1293", "4019", "1031", "209", "1693", "1735", "5261", "5345", "5429", "27649", "306659", "310619", "312929", "317549", "4155857", "4195897", "603091", "615961", "619393", "19304143", "19463731", "1228951", "9898103", "4982299", "1251116", "2524397", "10164083" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A001620", "A047994", "A177754", "A327837", "A370899", "A379517", "A379518", "A379519" ]
null
Amiram Eldar, Dec 24 2024
2024-12-24T07:27:22
oeisdata/seq/A379/A379517.seq
f9eb581838c009a9bb4a0e8f773063e8
A379518
Denominators of the partial sums of the reciprocals of the unitary totient function (A047994).
[ "1", "1", "2", "6", "12", "12", "4", "28", "56", "56", "280", "840", "280", "840", "210", "42", "336", "336", "1008", "1008", "1008", "5040", "55440", "55440", "55440", "55440", "720720", "720720", "102960", "102960", "102960", "3191760", "3191760", "199485", "1595880", "797940", "199485", "398970", "1595880", "11171160", "1117116", "279279" ]
[ "nonn", "easy", "frac" ]
7
1
3
[ "A047994", "A177754", "A370899", "A379517", "A379518", "A379520" ]
null
Amiram Eldar, Dec 24 2024
2024-12-24T07:26:46
oeisdata/seq/A379/A379518.seq
ff49c53f4053ce132ce2ed5b7092a1fb
A379519
Numerators of the partial alternating sums of the reciprocals of the unitary totient function (A047994).
[ "1", "0", "1", "1", "5", "-1", "1", "-5", "11", "-31", "-71", "-211", "-47", "-281", "-22", "-29", "-359", "-569", "-1427", "-1847", "-1427", "-1931", "-18721", "-22681", "-20371", "-24991", "-297163", "-37467", "-34607", "-44617", "-125843", "-4141373", "-3769001", "-2117233", "-327013", "-2117233", "-6041389", "-6662009", "-774568", "-3297757" ]
[ "sign", "easy", "frac" ]
7
1
5
[ "A047994", "A065442", "A177754", "A327837", "A370899", "A379517", "A379519", "A379520" ]
null
Amiram Eldar, Dec 24 2024
2024-12-24T07:26:25
oeisdata/seq/A379/A379519.seq
1f7573fab343cee66b8bcb2b4b2ec76b
A379520
Denominators of the partial alternating sums of the reciprocals of the unitary totient function (A047994).
[ "1", "1", "2", "6", "12", "12", "12", "84", "168", "168", "840", "840", "280", "840", "105", "105", "1680", "1680", "5040", "5040", "5040", "5040", "55440", "55440", "55440", "55440", "720720", "80080", "80080", "80080", "240240", "7447440", "7447440", "3723720", "620620", "3723720", "11171160", "11171160", "1396395", "5585580", "2234232", "2234232" ]
[ "nonn", "easy", "frac" ]
7
1
3
[ "A047994", "A177754", "A370899", "A379518", "A379519", "A379520" ]
null
Amiram Eldar, Dec 24 2024
2024-12-24T07:29:03
oeisdata/seq/A379/A379520.seq
00c1198fcd8002e01e5745182dea97d3
A379521
Expansion of (1/x) * Series_Reversion( x / ( (1+x)^3 * (1+2*x)^2 ) ).
[ "1", "7", "68", "767", "9425", "122436", "1653776", "22992655", "326863667", "4729547023", "69424933968", "1031309398852", "15474833826028", "234201961398776", "3570887895432504", "54799089019823407", "845757173849239415", "13119400228929684885", "204429551432900950068", "3198423097762769254279", "50225078058311068601425" ]
[ "nonn" ]
17
0
2
[ "A243659", "A379521", "A379522" ]
null
Seiichi Manyama, Dec 24 2024
2024-12-25T09:17:08
oeisdata/seq/A379/A379521.seq
dcc2dedc6bbef10644ef4503a30d1584
A379522
Expansion of (1/x) * Series_Reversion( x / ( (1+x)^3 * (1+2*x)^3 ) ).
[ "1", "9", "114", "1683", "27111", "462060", "8192078", "149541975", "2791795695", "53056724409", "1023021616920", "19963667407572", "393536736830724", "7824888965728584", "156750391932619254", "3160558799674447167", "64092227061832430895", "1306327265854324847595", "26746550927141536784370" ]
[ "nonn" ]
14
0
2
[ "A243659", "A379521", "A379522" ]
null
Seiichi Manyama, Dec 24 2024
2024-12-25T09:17:16
oeisdata/seq/A379/A379522.seq
5708ca4667c9be3d90f252fb4eec5d79
A379523
Sum of coreful divisors d | k such that gcd(d, k/d) > 1 and rad(d) = rad(k/d), with d | k/d and d < d/k, where k is in A320966 and rad = A007947.
[ "6", "10", "12", "30", "54", "18", "30", "24", "30", "126", "30", "30", "42", "120", "238", "90", "60", "56", "42", "50", "126", "60", "510", "162", "130", "168", "60", "336", "70", "150", "234", "66", "240", "110", "990", "90", "378", "432", "84", "132", "78", "112", "210", "270", "546", "90", "110", "456", "330", "150", "2046", "1092", "182", "714", "102", "350", "260" ]
[ "nonn" ]
31
1
1
[ "A000079", "A001221", "A007947", "A246549", "A320966", "A364988", "A379523" ]
null
Michael De Vlieger, Jan 15 2025
2025-01-19T09:29:50
oeisdata/seq/A379/A379523.seq
3e9be54be67810d5652b67b496712344
A379524
Minimal discriminants d of real quadratic number fields K = Q(sqrt(d)), d > 0, with elementary bicyclic 3-class group Cl_3(K)=(3,3) and second 3-class group M=Gal(F_3^2(K)/K) of assigned coclass cc(M)=1,2,3,4,...
[ "32009", "214712", "710652", "8127208", "180527768" ]
[ "nonn", "hard", "more" ]
34
1
1
[ "A269318", "A269319", "A379524" ]
null
Daniel Constantin Mayer, Dec 24 2024
2025-02-07T17:21:06
oeisdata/seq/A379/A379524.seq
be5ae8e6b5f5d1b724c26ff2269c3ae7
A379525
a(1) = 1. For n > 1, if a(n-1) is a novel term, a(n) = A003132(a(n-1)). If a(n-1) has been seen k (>1) times already, a(n) = k*a(n-1).
[ "1", "1", "2", "4", "16", "37", "58", "89", "145", "42", "20", "4", "8", "64", "52", "29", "85", "89", "178", "114", "18", "65", "61", "37", "74", "65", "130", "10", "1", "3", "9", "81", "65", "195", "107", "50", "25", "29", "58", "116", "38", "73", "58", "174", "66", "72", "53", "34", "25", "50", "100", "1", "4", "12", "5", "25", "75", "74", "148", "81", "162", "41", "17", "50", "150" ]
[ "nonn", "base" ]
15
1
3
[ "A003132", "A379525", "A379551" ]
null
David James Sycamore, Dec 24 2024
2024-12-26T20:08:09
oeisdata/seq/A379/A379525.seq
d3b8ba6447c05d35ffe7b016bc771a85
A379526
Number of ordered ways of writing 1 as Sum_{k=-n..n, k<>0} e(k)/k, where e(k) is 0 or 1.
[ "1", "7", "133", "5419", "383785", "42244765", "6520970371", "1359532454017" ]
[ "nonn", "more" ]
5
1
2
[ "A002967", "A038034", "A379335", "A379451", "A379526" ]
null
Ilya Gutkovskiy, Dec 24 2024
2024-12-26T04:43:35
oeisdata/seq/A379/A379526.seq
29bab1af60a47c87136e902fdef945af
A379527
Number of compositions (ordered partitions) of 1 into {1/1, 1/3, 1/5, ..., 1/(2*n-1)}.
[ "1", "2", "3", "4", "22", "23", "24", "5115", "5116", "5117", "1689273", "1689274", "441985160", "191869129330", "191869129331", "191869129332" ]
[ "nonn", "more" ]
22
1
2
[ "A005408", "A020473", "A038034", "A378269", "A379527" ]
null
Ilya Gutkovskiy, Dec 24 2024
2024-12-28T00:06:52
oeisdata/seq/A379/A379527.seq
d8d60fa3a1fd95852246eed24c56d95a
A379528
Number of compositions (ordered partitions) of 1 into {1/1^2, 1/2^2, 1/3^2, ..., 1/n^2}.
[ "1", "2", "3", "97", "98", "40917543", "40917544", "2901109178066823", "81221415992592163051371926", "373220766236315864054296758124337507430", "373220766236315864054296758124337507431" ]
[ "nonn", "more" ]
17
1
2
[ "A000290", "A020473", "A038034", "A348625", "A378270", "A378842", "A379528" ]
null
Ilya Gutkovskiy, Dec 24 2024
2024-12-28T03:06:28
oeisdata/seq/A379/A379528.seq
bfb794a44268e4cff51bd4ff48474363
A379529
a(0) = 0; for n>0, let MSD = Most Significant Digit and LSD = Least Significant Digit, set MSD(a(n)) = [10 - LSD(a(n-1))] mod 10 and let remaining digits of a(n) be such that a(n) is the least integer not yet present in the sequence. If LSD(a(n-1)) = 0 then the least integer not yet present in the sequence is chosen, whatever its MSD is.
[ "0", "1", "9", "10", "2", "8", "20", "3", "7", "30", "4", "6", "40", "5", "50", "11", "90", "12", "80", "13", "70", "14", "60", "15", "51", "91", "92", "81", "93", "71", "94", "61", "95", "52", "82", "83", "72", "84", "62", "85", "53", "73", "74", "63", "75", "54", "64", "65", "55", "56", "41", "96", "42", "86", "43", "76", "44", "66", "45", "57", "31", "97", "32", "87", "33", "77", "34", "67", "35" ]
[ "nonn", "easy", "base" ]
18
0
3
[ "A010879", "A379529" ]
null
Paolo P. Lava, Dec 24 2024
2025-01-07T10:09:25
oeisdata/seq/A379/A379529.seq
20169fb37950e7f634d2d1476699b710
A379530
a(n) = (A135318(3*n) + A135318(3*n+1) + A135318(3*n+2))/3.
[ "1", "3", "8", "23", "64", "185", "512", "1479", "4096", "11833", "32768", "94663", "262144", "757305", "2097152", "6058439", "16777216", "48467513", "134217728", "387740103", "1073741824", "3101920825", "8589934592", "24815366599", "68719476736", "198522932793", "549755813888", "1588183462343", "4398046511104", "12705467698745" ]
[ "nonn", "easy" ]
18
0
2
[ "A001018", "A013730", "A015565", "A135318", "A379530" ]
null
Paul Curtz, Dec 24 2024
2024-12-31T06:35:37
oeisdata/seq/A379/A379530.seq
329e2ef9ea87ea361bf08f8ac5718caa
A379531
Decimal expansion of (3*sqrt(6) - 7)*Pi/3.
[ "3", "6", "4", "9", "1", "6", "1", "2", "2", "5", "9", "5", "0", "0", "0", "3", "5", "0", "1", "8", "4", "7", "1", "6", "9", "3", "0", "3", "7", "3", "8", "6", "5", "0", "7", "2", "3", "4", "3", "5", "0", "2", "0", "7", "3", "5", "0", "9", "3", "0", "7", "0", "2", "3", "0", "0", "0", "1", "3", "3", "5", "9", "1", "8", "2", "0", "1", "5", "4", "6", "5", "9", "7", "4", "3", "6", "4", "4", "9", "4", "2", "7", "3", "4", "3", "0", "6", "9", "2", "1", "8", "4", "9", "4", "2", "6", "8", "1", "9", "1" ]
[ "nonn", "cons" ]
5
0
1
[ "A000796", "A010464", "A010507", "A019670", "A379531" ]
null
Stefano Spezia, Dec 24 2024
2024-12-24T12:59:21
oeisdata/seq/A379/A379531.seq
c81ef8f0697d1a48b09114f3cc1bb8b3
A379532
Ulam numbers that are products of exactly four distinct primes (or tetraprimes).
[ "390", "546", "690", "798", "1155", "1230", "1770", "2010", "2090", "2418", "2618", "2814", "3090", "3290", "3390", "3930", "4326", "4370", "4470", "4578", "4602", "4641", "6110", "6870", "7170", "7490", "7735", "7930", "8294", "9834", "10110", "10545", "10738", "11102", "11346", "11390", "11454", "11622", "11715", "11886", "12270", "12441", "12470", "12570" ]
[ "nonn" ]
13
1
1
[ "A002858", "A046386", "A068820", "A378795", "A379162", "A379532" ]
null
Massimo Kofler, Dec 24 2024
2025-01-03T14:55:08
oeisdata/seq/A379/A379532.seq
546654833093b82b545d09a1eda8a790
A379533
Decimal expansion of (sqrt(13) - 1)/36.
[ "0", "7", "2", "3", "7", "6", "4", "2", "4", "3", "1", "8", "4", "4", "4", "1", "4", "7", "0", "3", "1", "0", "8", "9", "4", "7", "9", "6", "5", "1", "9", "5", "8", "2", "2", "0", "7", "2", "9", "2", "0", "2", "6", "8", "2", "6", "0", "6", "8", "1", "2", "3", "9", "4", "7", "9", "7", "5", "1", "2", "5", "8", "4", "8", "9", "5", "1", "9", "9", "0", "8", "1", "8", "9", "7", "0", "2", "8", "0", "6", "7", "9", "2", "2", "3", "5", "0", "5", "3", "0", "0", "5", "6", "0", "6", "9", "1", "8", "6", "6", "0" ]
[ "nonn", "cons", "easy" ]
14
0
2
[ "A010470", "A248866", "A343851", "A379533", "A379534" ]
null
Stefano Spezia, Dec 24 2024
2025-04-03T04:08:32
oeisdata/seq/A379/A379533.seq
016242187b10f1035a9f6d2ecfc92430
A379534
Decimal expansion of (9*sqrt(65) - 55)/320.
[ "0", "5", "4", "8", "7", "5", "9", "9", "9", "1", "7", "0", "8", "9", "6", "7", "0", "8", "9", "7", "2", "8", "1", "0", "9", "9", "7", "1", "0", "2", "2", "9", "3", "5", "6", "3", "0", "6", "3", "1", "5", "4", "8", "9", "6", "0", "9", "5", "2", "4", "1", "1", "2", "6", "5", "3", "5", "7", "1", "6", "6", "6", "0", "9", "4", "8", "0", "4", "6", "4", "8", "2", "9", "9", "7", "5", "9", "7", "4", "8", "0", "7", "0", "8", "2", "5", "4", "3", "3", "8", "7", "5", "1", "4", "2", "2", "1", "1", "1", "8", "5" ]
[ "nonn", "cons", "easy" ]
14
0
2
[ "A010517", "A248866", "A343851", "A379533", "A379534" ]
null
Stefano Spezia, Dec 24 2024
2025-04-03T04:09:04
oeisdata/seq/A379/A379534.seq
c2ae7bc4627db060b1fc1ea132f8826f
A379535
a(n) is the least number that has n prime factors, counted by multiplicity, and n runs in its decimal representation.
[ "2", "10", "102", "1012", "10104", "101010", "1010124", "10101216", "101010176", "1010101504", "10101010304", "101010101248", "1010101013280", "10101010101248", "101010101013504", "1010101010137856", "10101010101010432", "101010101010145280", "1010101010101010432", "10101010101010497536", "101010101010101084160", "1010101010101010620416", "10101010101010105368576" ]
[ "nonn", "base" ]
22
1
1
[ "A001222", "A043096", "A043562", "A379229", "A379535" ]
null
Robert Israel, Jan 07 2025
2025-01-07T10:05:04
oeisdata/seq/A379/A379535.seq
a456ae1eb7170ab546299ef23add3332
A379536
Rectangular array, read by descending antidiagonals: the Type 1 runlength index array of A378142; see Comments.
[ "1", "6", "2", "7", "12", "3", "11", "14", "18", "4", "13", "17", "21", "25", "5", "16", "20", "24", "39", "28", "8", "19", "23", "36", "55", "40", "29", "9", "22", "35", "50", "72", "56", "41", "30", "10", "26", "49", "71", "92", "73", "61", "42", "31", "15", "27", "52", "87", "103", "93", "78", "62", "45", "32", "33", "34", "54", "102", "124", "104", "94", "79", "65", "46", "47", "166", "37", "58", "113", "135", "125", "105", "97", "84", "66", "99", "179", "618" ]
[ "nonn", "tabl" ]
16
1
2
[ "A000002", "A378142", "A379046", "A379536" ]
null
Clark Kimberling, Jan 11 2025
2025-01-20T22:45:35
oeisdata/seq/A379/A379536.seq
01e365b8053cba8e6b3f218950bd45ce
A379537
Frugal numbers in base 2: numbers k such that A377369(k) < A070939(k).
[ "1", "27", "32", "49", "64", "81", "121", "125", "128", "135", "147", "162", "169", "189", "192", "243", "250", "256", "289", "297", "320", "338", "343", "351", "361", "363", "375", "384", "405", "448", "486", "507", "512", "513", "529", "539", "567", "576", "578", "605", "621", "625", "637", "640", "648", "675", "686", "704", "722", "729", "750", "768", "783", "832" ]
[ "nonn", "base" ]
18
1
2
[ "A046759", "A070939", "A377369", "A379373", "A379537", "A379538" ]
null
Paolo Xausa, Dec 25 2024
2025-01-01T18:13:29
oeisdata/seq/A379/A379537.seq
1b1d5c62314366ae86eea6a6c5259eb7
A379538
Square array read by ascending antidiagonals: T(n,k) is the k-th frugal number in base n.
[ "1", "1", "27", "1", "32", "32", "1", "27", "49", "49", "1", "27", "64", "64", "64", "1", "81", "81", "81", "81", "81", "1", "64", "125", "125", "121", "98", "121", "1", "64", "81", "243", "128", "125", "121", "125", "1", "81", "81", "125", "250", "162", "128", "125", "128", "1", "125", "125", "125", "243", "256", "169", "169", "128", "135", "1", "125", "128", "128", "128", "343", "289", "243", "243", "169", "147" ]
[ "nonn", "tabl", "base" ]
24
2
3
[ "A046759", "A377478", "A379373", "A379537", "A379538", "A379539" ]
null
Paolo Xausa, Dec 25 2024
2025-01-01T09:49:42
oeisdata/seq/A379/A379538.seq
00a17a1615fbf029a7bb2340b33c28ba
A379539
a(n) is the (n-1)-st frugal number in base n.
[ "1", "32", "64", "125", "250", "343", "343", "625", "729", "1024", "1849", "2197", "2401", "3125", "4374", "5103", "6250", "7168", "8704", "9477", "11875", "13718", "15379", "17303", "20577", "22627", "24334", "27889", "30613", "32805", "36501", "39601", "45056", "50301", "53125", "59392", "63869", "69169", "75449", "78125", "85169", "89667", "94249" ]
[ "nonn", "base" ]
6
2
2
[ "A379538", "A379539" ]
null
Paolo Xausa, Dec 25 2024
2024-12-30T16:57:54
oeisdata/seq/A379/A379539.seq
b61357b0334313c6d545a6c83436ca1f
A379540
Row sums of A376832.
[ "0", "0", "3", "16", "60", "168", "385", "768", "1386", "2320", "3663", "5520", "8008", "11256", "15405", "20608", "27030", "34848", "44251", "55440", "68628", "84040", "101913", "122496", "146050", "172848", "203175", "237328", "275616", "318360", "365893", "418560", "476718", "540736", "610995", "687888", "771820", "863208", "962481", "1070080", "1186458" ]
[ "nonn", "easy" ]
5
0
3
[ "A376832", "A379540" ]
null
Stefano Spezia, Dec 24 2024
2024-12-26T10:16:03
oeisdata/seq/A379/A379540.seq
dad03caaca95a6eac41e8be12912545d
A379541
Prime numbers such that the next greatest prime power is also prime.
[ "2", "5", "11", "17", "19", "29", "37", "41", "43", "53", "59", "67", "71", "73", "83", "89", "97", "101", "103", "107", "109", "131", "137", "139", "149", "151", "157", "163", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239", "257", "263", "269", "271", "277", "281", "293", "307", "311", "313", "317", "331", "347", "349", "353" ]
[ "nonn" ]
7
1
1
[ "A000015", "A000040", "A000961", "A001223", "A025474", "A031218", "A053607", "A057820", "A065514", "A067871", "A068315", "A080769", "A131605", "A178700", "A246655", "A274605", "A304521", "A345531", "A366833", "A366835", "A377281", "A377286", "A377287", "A377289", "A378368", "A379155", "A379156", "A379157", "A379158", "A379541" ]
null
Gus Wiseman, Dec 24 2024
2024-12-25T00:50:49
oeisdata/seq/A379/A379541.seq
5a37bb4e78a9f0a3958ce6246b267caa
A379542
Second term of the n-th differences of the prime numbers.
[ "3", "2", "0", "2", "-6", "14", "-30", "62", "-122", "220", "-344", "412", "-176", "-944", "4112", "-11414", "26254", "-53724", "100710", "-175034", "281660", "-410896", "506846", "-391550", "-401486", "2962260", "-9621128", "24977308", "-57407998", "120867310", "-236098336", "428880422", "-719991244", "1096219280" ]
[ "sign" ]
12
0
1
[ "A000040", "A001223", "A002808", "A007442", "A008578", "A030016", "A036263", "A053445", "A064113", "A065890", "A073445", "A073783", "A075526", "A084758", "A095195", "A140119", "A173390", "A175804", "A258025", "A258026", "A281425", "A293467", "A320590", "A333214", "A333254", "A376682", "A377033", "A377034", "A377036", "A377037", "A377038", "A377041", "A377046", "A377051", "A379542" ]
null
Gus Wiseman, Jan 12 2025
2025-01-12T23:55:18
oeisdata/seq/A379/A379542.seq
10e6c9d9ab980e8927d809d1f69844e2
A379543
Least number x such that there are exactly n multisets of positive integers > 1 with sum + product = x. Position of first appearance of n in A379669.
[ "2", "1", "8", "14", "24", "69", "84", "76", "59", "179", "195", "159", "314", "449", "384", "984", "467", "359", "909", "744", "839" ]
[ "nonn", "more" ]
6
0
1
[ "A000009", "A000041", "A001055", "A002865", "A025147", "A045778", "A069016", "A111133", "A318950", "A319000", "A379543", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379720", "A379839", "A379840", "A379841", "A379842", "A379843" ]
null
Gus Wiseman, Jan 15 2025
2025-01-15T23:51:20
oeisdata/seq/A379/A379543.seq
cff5b63dc1f4ac76abec828c7c01a087
A379544
a(n) = ((p-1)^n + (p+1)^n) mod p^2, where p is the n-th prime.
[ "0", "2", "5", "2", "110", "2", "238", "2", "414", "2", "682", "2", "1066", "2", "1410", "2", "2006", "2", "2546", "2", "3066", "2", "3818", "2", "4850", "2", "5562", "2", "6322", "2", "7874", "2", "9042", "2", "10430", "2", "11618", "2", "13026", "2", "14678", "2", "16426", "2", "17730", "2", "19834", "2", "22246", "2", "23766", "2", "25546", "2", "28270", "2", "30666" ]
[ "nonn" ]
24
1
2
null
null
Do Thanh Nhan, Dec 24 2024
2025-01-07T10:04:50
oeisdata/seq/A379/A379544.seq
4e348ac8877ec2e335f6ad0604ba139e
A379545
Triangle read by rows where row n lists powerful divisors d | n (i.e., d in A001694).
[ "1", "1", "1", "1", "4", "1", "1", "1", "1", "4", "8", "1", "9", "1", "1", "1", "4", "1", "1", "1", "1", "4", "8", "16", "1", "1", "9", "1", "1", "4", "1", "1", "1", "1", "4", "8", "1", "25", "1", "1", "9", "27", "1", "4", "1", "1", "1", "1", "4", "8", "16", "32", "1", "1", "1", "1", "4", "9", "36", "1", "1", "1", "1", "4", "8", "1", "1", "1", "1", "4", "1", "9", "1", "1", "1", "4", "8", "16", "1", "49", "1", "25", "1", "1", "4" ]
[ "nonn", "tabf", "easy" ]
27
1
5
[ "A000005", "A001694", "A005361", "A007947", "A027750", "A332785", "A379545", "A380819" ]
null
Michael De Vlieger, Feb 13 2025
2025-02-16T23:01:44
oeisdata/seq/A379/A379545.seq
e73f4252b090594628bb78d9a42502ee
A379546
Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^3 ) ).
[ "1", "8", "89", "1150", "16190", "240966", "3729185", "59404934", "967608590", "16041857672", "269807678442", "4592326407908", "78954271935856", "1369136489157250", "23918810207745777", "420575805001923782", "7437459126200243030", "132190772588551036800", "2360148586461490077870" ]
[ "nonn" ]
14
0
2
[ "A003168", "A371398", "A371406", "A371669", "A379522", "A379546", "A379547" ]
null
Seiichi Manyama, Dec 25 2024
2024-12-25T09:17:12
oeisdata/seq/A379/A379546.seq
c1a73555098d79548146fbe1e71b2072
A379547
Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^4 ) ).
[ "1", "10", "141", "2318", "41586", "789404", "15588677", "316957910", "6591000606", "139521610540", "2996554128002", "65135251885164", "1430214488595340", "31676376789702720", "706819317765805461", "15874751837921964646", "358585244386746378166", "8141109472248910295708" ]
[ "nonn" ]
14
0
2
[ "A003168", "A371406", "A379546", "A379547" ]
null
Seiichi Manyama, Dec 25 2024
2024-12-25T09:16:57
oeisdata/seq/A379/A379547.seq
b6f4429254a13093d694c20dea2f469a
A379548
a(1) = 1. For n > 1, a(n) is the earliest novel squarefree number divisible by the smallest prime which does not divide a(n-1).
[ "1", "2", "3", "6", "5", "10", "15", "14", "21", "22", "30", "7", "26", "33", "34", "39", "38", "42", "35", "46", "51", "58", "57", "62", "66", "55", "70", "69", "74", "78", "65", "82", "87", "86", "93", "94", "102", "85", "106", "105", "110", "111", "114", "95", "118", "123", "122", "129", "130", "138", "115", "134", "141", "142", "159", "146", "165", "154", "174", "145", "158" ]
[ "nonn" ]
15
1
2
[ "A005117", "A351495", "A379548" ]
null
David James Sycamore, Dec 25 2024
2024-12-28T18:21:21
oeisdata/seq/A379/A379548.seq
7158e4779dc81c8b7bd8be6d24a93f6e
A379549
Number of minimal edge covers in the n X n white bishop graph.
[ "1", "2", "117", "11614" ]
[ "nonn", "more" ]
4
2
2
null
null
Eric W. Weisstein, Dec 25 2024
2024-12-26T10:14:04
oeisdata/seq/A379/A379549.seq
f0e2962175fd3fa42e3dc4a11abc8218
A379550
Number of minimal edge covers in the n-trapezohedral graph.
[ "49", "189", "651", "2138", "6847" ]
[ "nonn", "more" ]
4
3
1
null
null
Eric W. Weisstein, Dec 25 2024
2024-12-26T10:14:07
oeisdata/seq/A379/A379550.seq
2e99d52b01b3132129dcc7060f71975c
A379551
Number of partitions of prime(n) into squares.
[ "1", "1", "2", "2", "4", "6", "9", "10", "14", "26", "28", "46", "60", "66", "84", "124", "169", "192", "256", "311", "347", "455", "545", "713", "993", "1167", "1255", "1466", "1590", "1846", "3042", "3491", "4279", "4564", "6312", "6712", "8094", "9697", "10923", "13027", "15460", "16368", "21585", "22795", "25392", "26778", "36651", "49641", "54801", "57560" ]
[ "nonn" ]
12
1
3
[ "A000040", "A001156", "A379551" ]
null
David James Sycamore, Dec 25 2024
2024-12-26T14:03:52
oeisdata/seq/A379/A379551.seq
ce40561fd0ed3b9a0deb8ed60090c86f
A379552
Number of pairs (d, k/d), d < k/d, such that d|k, rad(d) = rad(k/d) = rad(k), but d|k/d, for k = A376936(n), where rad = A007947.
[ "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "1", "3", "2", "2", "1", "2", "1", "1", "2", "3", "4", "2", "1", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "4", "4", "3", "1", "1", "3", "1", "1", "1", "2", "3", "1", "1", "2", "2", "4", "1", "2", "1", "3", "4", "1", "2", "6", "1", "3", "1", "3", "1", "1", "2", "1", "1", "1", "1", "2", "1", "4", "2", "2", "1", "2", "3", "1", "4", "2", "1", "1", "2", "1", "1", "3", "4" ]
[ "nonn", "easy" ]
9
1
4
[ "A007947", "A126706", "A376936", "A379552", "A379553", "A379554" ]
null
Michael De Vlieger, Dec 25 2024
2024-12-28T09:14:20
oeisdata/seq/A379/A379552.seq
e8ac8111563c2f8b1470666e495fe83b
A379553
Numbers k in A376936 that set records in A379552.
[ "216", "864", "3456", "7776", "31104", "124416", "279936", "497664", "972000", "1944000", "3888000", "7776000", "11664000", "15552000", "31104000", "34992000", "46656000", "62208000", "77760000", "97200000", "194400000", "291600000", "388800000", "777600000", "874800000", "1166400000", "1555200000", "3110400000", "3499200000" ]
[ "nonn" ]
8
1
1
[ "A376936", "A379552", "A379553", "A379554" ]
null
Michael De Vlieger, Dec 25 2024
2024-12-30T17:09:44
oeisdata/seq/A379/A379553.seq
1267f954ab604a7cf9fd97964a299f0c
A379554
Records in A379552.
[ "1", "2", "3", "4", "6", "8", "9", "10", "12", "14", "18", "20", "21", "24", "26", "27", "28", "30", "32", "36", "40", "42", "48", "52", "54", "56", "60", "64", "72", "78", "80", "90", "96", "100", "108", "114", "120", "126", "128", "135", "136", "144", "150", "160", "168", "170", "176", "180", "186", "192", "200", "204", "210", "224", "240", "248", "252", "264", "272", "280", "288" ]
[ "nonn" ]
6
1
2
[ "A376936", "A379552", "A379553", "A379554" ]
null
Michael De Vlieger, Dec 25 2024
2024-12-30T17:09:57
oeisdata/seq/A379/A379554.seq
0cb1cab98be0f561e4e5577a16b9df84
A379555
Row products of the triangle A330613.
[ "1", "1", "10", "312", "19800", "2112320", "339721200", "76736721600", "23161613673856", "9002333397657600", "4378779743334796800", "2605462349704907264000", "1861650500340096385920000", "1572904258939213777572323328", "1551130967414603865237595648000", "1765646154517023983944233381888000", "2297658475440816396798100972400640000" ]
[ "nonn" ]
7
0
3
[ "A227514", "A330613", "A379555" ]
null
Stefano Spezia, Dec 25 2024
2024-12-26T10:16:17
oeisdata/seq/A379/A379555.seq
0027ad9ead612ee5fcd839f23ed6dd81
A379556
Decimal expansion of the square root of 5312.
[ "7", "2", "8", "8", "3", "4", "6", "8", "6", "3", "3", "1", "5", "4", "3", "9", "1", "0", "5", "5", "5", "6", "5", "0", "0", "8", "8", "3", "7", "5", "0", "9", "3", "5", "3", "5", "2", "0", "7", "9", "3", "1", "1", "3", "3", "4", "6", "1", "1", "9", "6", "4", "6", "8", "1", "9", "9", "7", "5", "5", "0", "7", "7", "2", "0", "5", "2", "8", "1", "6", "9", "5", "5", "4", "2", "6", "7", "2", "4", "5", "3", "2", "4", "6", "8", "2", "7", "3", "1", "6", "8", "7", "4", "3", "3", "4", "1", "7", "9", "7", "3", "9", "1", "3", "9", "7", "5", "4", "1", "0", "7", "0", "0", "6", "4", "5", "5", "9", "7", "0", "2", "1", "7", "5", "1", "0", "6", "6" ]
[ "nonn", "cons", "easy" ]
17
2
1
[ "A010534", "A379556" ]
null
Alonso del Arte, Dec 25 2024.
2025-01-02T12:22:03
oeisdata/seq/A379/A379556.seq
1982493c08f5783b1c6fad52926ebe3f
A379557
Number k such that A379442(k) = k.
[ "1", "2", "30", "285", "750", "822", "826", "952", "2824", "3016", "6112" ]
[ "nonn", "more" ]
6
1
2
[ "A379292", "A379442", "A379557", "A379558", "A379559" ]
null
Scott R. Shannon, Dec 25 2024
2024-12-26T10:17:20
oeisdata/seq/A379/A379557.seq
b7afc66275d7e52eadfe84498ba99619
A379558
Index where prime(n) appears as a term in A379442.
[ "2", "6", "17", "25", "77", "83", "89", "259", "319", "329", "539", "545", "1010", "1016", "1026", "1032", "2128", "2134", "2140", "2146", "2152", "2158", "3196", "3202", "3222", "3228", "3234", "5465", "5471", "5487", "5493", "6300", "6308", "6314", "6320", "8252", "8258", "8264", "8270", "8276", "8282", "8288", "13775", "13949", "13957", "13965", "13971", "13977", "13983", "13989", "13995", "14001", "27677", "27683", "27689", "27695", "27701", "27707", "27713", "27719" ]
[ "nonn" ]
11
1
1
[ "A379290", "A379442", "A379557", "A379558", "A379559" ]
null
Scott R. Shannon, Dec 25 2024
2025-01-06T08:59:13
oeisdata/seq/A379/A379558.seq
43a7838a29bd9b8c84aff5a94d5c75f1
A379559
Index where n appears as a term in A379442.
[ "1", "2", "6", "3", "17", "4", "25", "9", "5", "15", "77", "8", "83", "13", "19", "10", "89", "7", "259", "12", "23", "28", "319", "11", "16", "34", "21", "27", "329", "30", "539", "40", "56", "36", "73", "31", "545", "46", "58", "38", "1010", "32", "1016", "14", "22", "48", "1026", "39", "24", "18", "60", "29", "1032", "64", "79", "44", "62", "52", "2128", "35", "2134", "50", "20", "41", "81", "54", "2140", "33", "97", "71", "2146", "69", "2152", "103", "72", "37", "75", "101", "2158", "43", "65", "107", "3196", "47" ]
[ "nonn" ]
12
1
2
[ "A379293", "A379442", "A379557", "A379558", "A379559" ]
null
Scott R. Shannon, Dec 25 2024
2025-01-06T08:59:17
oeisdata/seq/A379/A379559.seq
ce3e8a95e2f077a725404a189b7b1b75
A379560
a(1) = 1, a(2) = 4; for n > 2, a(n) is the smallest unused positive nonsquarefree number that shares a factor with a(n-1).
[ "1", "4", "8", "12", "9", "18", "16", "20", "24", "27", "36", "28", "32", "40", "25", "45", "48", "44", "50", "52", "54", "56", "49", "63", "60", "64", "68", "72", "75", "80", "76", "84", "81", "90", "88", "92", "96", "98", "100", "104", "108", "99", "117", "120", "112", "116", "124", "126", "128", "132", "121", "176", "136", "140", "125", "135", "144", "147", "150", "148", "152", "156", "153", "162", "160", "164", "168", "171", "180", "172", "184", "188", "192", "189", "175", "196", "198", "200", "204", "207", "216" ]
[ "nonn" ]
8
1
2
[ "A013929", "A064413", "A100113", "A379248", "A379560" ]
null
Scott R. Shannon, Dec 26 2024
2024-12-26T10:14:49
oeisdata/seq/A379/A379560.seq
bd536ab71ab8de00e1477fbb2139848e
A379561
a(n) = A003418(n+1)*H(n), where H(n) = 1 + 1/2 + ... + 1/n is the n-th harmonic number.
[ "2", "9", "22", "125", "137", "1029", "2178", "6849", "7129", "81191", "83711", "1118273", "1145993", "1171733", "2391514", "41421503", "42142223", "813635157", "825887397", "837527025", "848612385", "19761458895", "19994251455", "101086721625", "102157567401", "309561680403", "312536252003", "9146733078187" ]
[ "nonn" ]
131
1
1
[ "A000203", "A001008", "A002805", "A003418", "A025529", "A025558", "A027457", "A077761", "A152648", "A193758", "A206431", "A379561" ]
null
Miko Labalan, Dec 26 2024
2025-02-05T16:56:34
oeisdata/seq/A379/A379561.seq
d9a22228d7d95dff7281c34ffb356920
A379562
Number of compositions (ordered partitions) of 1 into {1/1^3, 1/2^3, 1/3^3, ..., 1/n^3}.
[ "1", "2", "3", "272335", "272336" ]
[ "nonn", "more" ]
8
1
2
[ "A000578", "A020473", "A038034", "A378271", "A379528", "A379562" ]
null
Ilya Gutkovskiy, Dec 26 2024
2025-01-08T07:11:42
oeisdata/seq/A379/A379562.seq
6d8b3bda3804061adefd40dbae3662ea
A379563
Smallest degree of x with the largest coefficient in Product_{k=1..n} (1 + x^prime(k)).
[ "0", "0", "0", "5", "5", "5", "18", "18", "35", "42", "58", "73", "89", "114", "137", "163", "190", "220", "249", "281", "318", "356", "393", "437", "480", "530", "580", "632", "685", "740", "796", "860", "925", "994", "1063", "1138", "1213", "1292", "1373", "1457", "1543", "1633", "1723", "1819", "1915", "2014", "2113", "2219", "2330", "2444", "2558", "2675", "2794", "2915", "3040", "3169" ]
[ "nonn" ]
5
0
4
[ "A000586", "A350393", "A350457", "A379563", "A379564" ]
null
Ilya Gutkovskiy, Dec 26 2024
2025-01-07T10:20:47
oeisdata/seq/A379/A379563.seq
8917077e3b1a5c5985657f5038c56444
A379564
Largest degree of x with the largest coefficient in Product_{k=1..n} (1 + x^prime(k)).
[ "0", "2", "5", "5", "12", "23", "23", "40", "42", "58", "71", "87", "108", "124", "144", "165", "191", "220", "252", "287", "321", "356", "398", "437", "483", "530", "581", "632", "686", "740", "797", "860", "926", "994", "1064", "1138", "1214", "1292", "1374", "1457", "1544", "1633", "1724", "1819", "1916", "2014", "2114", "2219", "2331", "2444", "2559", "2675", "2795", "2915", "3041", "3169" ]
[ "nonn" ]
4
0
2
[ "A000586", "A350394", "A350457", "A379563", "A379564" ]
null
Ilya Gutkovskiy, Dec 26 2024
2025-01-07T10:20:57
oeisdata/seq/A379/A379564.seq
461305d48730db13fbd902a70e4ffd3c
A379565
Decimal expansion of (2/3)*x where x is the real solution of the equation x^2 + 2*sqrt(1 - x^2) = 2*x*(x + arccos(x)).
[ "4", "2", "7", "8", "7", "3", "3", "9", "7", "1", "2", "4", "7", "2", "8", "0", "1", "6", "4", "4", "4", "0", "3", "7", "0", "0", "6", "4", "4", "6", "6", "5", "2", "6", "5", "7", "7", "8", "0", "6", "0", "7", "5", "9", "4", "6", "6", "3", "3", "6", "1", "2", "6", "2", "7", "6", "8", "8", "6", "6", "2", "8", "3", "0", "5", "6", "4", "8", "5", "7", "3", "8", "2", "1", "9", "7", "1", "1", "5", "9", "5", "9", "1", "7", "4", "9", "7", "2", "9", "3", "1", "1", "7", "5", "8", "0", "1", "9", "0", "0" ]
[ "nonn", "cons" ]
4
0
1
[ "A244054", "A379565" ]
null
Stefano Spezia, Dec 26 2024
2024-12-26T13:35:43
oeisdata/seq/A379/A379565.seq
4b8380d776523f73ae9ef8cdef95aec8
A379566
Number of n-digit numbers that have exactly 3 divisors.
[ "2", "2", "7", "14", "40", "103", "278", "783", "2172", "6191", "17701", "51205", "149149", "436932", "1287378", "3809498", "11321211", "33764868", "101029398", "303175579", "912147300", "2750855002", "8313825647", "25176031558", "76375623757", "232082001064", "706304629714", "2152571584249", "6568923555719" ]
[ "nonn", "base" ]
14
1
1
[ "A001248", "A006880", "A122121", "A284398", "A379566" ]
null
Seiichi Manyama, Dec 26 2024
2024-12-26T10:15:28
oeisdata/seq/A379/A379566.seq
f2c643f8cc0e93d0fda1f6aa256ad833
A379567
Number of n-digit numbers that have exactly 4 divisors.
[ "2", "30", "260", "2316", "20719", "186565", "1694033", "15522194", "143359184", "1332981873", "12466196499", "117165976234", "1105961883514", "10478813824875", "99613913708218", "949727471728542" ]
[ "nonn", "more", "base" ]
13
1
1
[ "A035533", "A284398", "A379567" ]
null
Seiichi Manyama, Dec 26 2024
2024-12-26T10:15:23
oeisdata/seq/A379/A379567.seq
e1afe0547d8d48bc5a0b911b41eab20e
A379568
Number of n-digit numbers that have exactly 5 divisors.
[ "0", "2", "1", "1", "3", "4", "5", "9", "15", "25", "37", "66", "107", "171", "293", "490", "810", "1362", "2302", "3889", "6552", "11149", "18950", "32255", "55053", "94096", "161036", "275896", "473709", "813669", "1399593", "2409905", "4154437", "7166774", "12375776", "21389092", "36994679", "64034719", "110918422", "192257157", "333449674", "578697626" ]
[ "nonn", "base" ]
28
1
2
[ "A006880", "A284398", "A379566", "A379568" ]
null
Seiichi Manyama, Dec 26 2024
2024-12-30T04:27:48
oeisdata/seq/A379/A379568.seq
b1c47c59778c7ec050060f044346b940
A379569
Number of n-digit numbers that have exactly 6 divisors.
[ "0", "16", "94", "654", "4863", "38243", "313705", "2658846", "23073712", "203859889", "1826368510", "16544195786", "151222451513", "1392635179004", "12906366376283", "120260052661235" ]
[ "nonn", "more", "base" ]
24
1
2
[ "A030515", "A284398", "A379569" ]
null
Seiichi Manyama, Dec 26 2024
2025-01-02T12:17:10
oeisdata/seq/A379/A379569.seq
a0272dbc4ee81fdb6f8edb866d77712f
A379570
Number of n-digit numbers that have exactly 8 divisors.
[ "0", "10", "170", "1934", "20067", "202246", "2003991", "19674052", "192215670", "1873532828", "18242642732", "177582019015", "1728951136938", "16840198807124", "164117159854744", "1600427660469575", "15617400806292160" ]
[ "nonn", "more", "base" ]
28
1
2
[ "A215218", "A284398", "A379570" ]
null
Seiichi Manyama, Dec 26 2024
2025-01-02T12:17:28
oeisdata/seq/A379/A379570.seq
988662f3278f8b965384d3159814e309
A379571
Number of minimal total dominating sets in the n-Pell graph.
[ "1", "2", "30", "18128" ]
[ "nonn", "more" ]
4
1
2
null
null
Eric W. Weisstein, Dec 26 2024
2024-12-26T10:15:32
oeisdata/seq/A379/A379571.seq
2bedc5b4856c9bda9889f8e5af1de5c6
A379572
Number of uniquely graceful graphs containing no isolated points.
[ "0", "1", "2", "4", "1", "5", "10", "29" ]
[ "nonn", "more" ]
8
1
3
[ "A379572", "A379573", "A379574" ]
null
Eric W. Weisstein, Dec 26 2024
2024-12-31T11:14:52
oeisdata/seq/A379/A379572.seq
68fa24e3e8cf54f091e4cc0cab0f07e9
A379573
Numbers of connected uniquely graceful graph on n vertices.
[ "1", "1", "2", "4", "1", "4", "2", "19" ]
[ "nonn", "more" ]
8
1
3
[ "A379572", "A379573", "A379574" ]
null
Eric W. Weisstein, Dec 26 2024
2024-12-31T11:14:56
oeisdata/seq/A379/A379573.seq
0966940e97f6cbc2ad9e49a4a75fc305
A379574
Numbers of (not necessarily connected) uniquely graceful graphs on n vertices.
[ "1", "1", "2", "5", "2", "5", "11", "33" ]
[ "nonn", "more" ]
8
1
3
[ "A379572", "A379573", "A379574" ]
null
Eric W. Weisstein, Dec 26 2024
2024-12-31T11:15:01
oeisdata/seq/A379/A379574.seq
34109214c90d8d01d3f8ef2efed34062
A379575
Total numbers of fundamentally distinct graceful labelings among all simple graphs on n vertices having no isolated points.
[ "0", "1", "2", "13", "157", "3292", "110578", "5903888" ]
[ "nonn", "more" ]
9
1
3
[ "A333727", "A379575", "A379576" ]
null
Eric W. Weisstein, Dec 26 2024
2024-12-31T11:15:09
oeisdata/seq/A379/A379575.seq
235d37b138b2d4c8d35d6237239f0815
A379576
Total numbers of fundamentally distinct graceful labelings of all simple graphs on n vertices.
[ "1", "1", "2", "14", "174", "3655", "122439", "6470268" ]
[ "nonn", "more" ]
15
1
3
[ "A333727", "A379575", "A379576" ]
null
Eric W. Weisstein, Dec 26 2024
2024-12-31T14:37:22
oeisdata/seq/A379/A379576.seq
9b4f3ed23b281bc4512ee5168033286d
A379577
a(n) = (n!)^n + n^n.
[ "2", "2", "8", "243", "332032", "24883203125", "139314069504046656", "82606411253903523840823543", "6984964247141514123629140377616777216", "109110688415571316480344899355894085582848387420489", "395940866122425193243875570782668457763038822400000000010000000000", "409933016554924328182440935903164918932547530146724293451448320000000000285311670611" ]
[ "nonn", "easy" ]
16
0
1
[ "A000142", "A000312", "A036740", "A379577" ]
null
Ctibor O. Zizka, Dec 26 2024
2024-12-30T06:20:48
oeisdata/seq/A379/A379577.seq
cc1d52f9657ff3c391d621de5ea83380
A379578
In the base-4 expansion of n map 0->1, 1->3, 2->0, 3->2.
[ "1", "3", "0", "2", "13", "15", "12", "14", "1", "3", "0", "2", "9", "11", "8", "10", "53", "55", "52", "54", "61", "63", "60", "62", "49", "51", "48", "50", "57", "59", "56", "58", "5", "7", "4", "6", "13", "15", "12", "14", "1", "3", "0", "2", "9", "11", "8", "10", "37", "39", "36", "38", "45", "47", "44", "46", "33", "35", "32", "34", "41", "43", "40", "42", "213", "215", "212", "214", "221" ]
[ "nonn", "base", "easy", "look" ]
49
0
2
[ "A000225", "A020988", "A035327", "A379578" ]
null
Darío Clavijo, Dec 26 2024
2025-01-06T20:03:29
oeisdata/seq/A379/A379578.seq
e0a739c1544251dc5e90ed72ba459e5d
A379579
Numerators of the partial sums of the reciprocals of the powerfree part function (A055231).
[ "1", "3", "11", "17", "91", "16", "117", "152", "187", "381", "4261", "13553", "178499", "90322", "30441", "35446", "607587", "1300259", "24875091", "25521737", "77027101", "38733998", "895731799", "932913944", "1044460379", "2097501253", "2320594123", "2352464533", "68444564327", "11443370128", "355822756173", "389249504528" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A055231", "A328013", "A370900", "A370901", "A379579", "A379580", "A379581" ]
null
Amiram Eldar, Dec 26 2024
2024-12-26T20:02:19
oeisdata/seq/A379/A379579.seq
ced1daabd7b51ad13fc4115dbc6a1e0c
A379580
Denominators of the partial sums of the reciprocals of the powerfree part function (A055231).
[ "1", "2", "6", "6", "30", "5", "35", "35", "35", "70", "770", "2310", "30030", "15015", "5005", "5005", "85085", "170170", "3233230", "3233230", "9699690", "4849845", "111546435", "111546435", "111546435", "223092870", "223092870", "223092870", "6469693230", "1078282205", "33426748355", "33426748355", "9116385915", "18232771830" ]
[ "nonn", "easy", "frac" ]
6
1
2
[ "A055231", "A370900", "A370901", "A379579", "A379580", "A379582" ]
null
Amiram Eldar, Dec 26 2024
2024-12-26T20:02:30
oeisdata/seq/A379/A379580.seq
48dcb069c070a9ae3b80c287f97ccbc8
A379581
Numerators of the partial alternating sums of the reciprocals of the powerfree part function (A055231).
[ "1", "1", "5", "-1", "1", "-2", "1", "-104", "1", "-19", "1", "-769", "-7687", "-4916", "-261", "-1262", "-20453", "-57923", "-1066503", "-5979161", "-17475593", "-8958244", "-201189767", "-79457304", "-42275159", "-87410483", "-13046193", "-23669663", "-612055937", "-1025912126", "-28568429291", "-128848674356", "-125809879051" ]
[ "sign", "easy", "frac" ]
8
1
3
[ "A055231", "A328013", "A370900", "A370901", "A379579", "A379581", "A379582" ]
null
Amiram Eldar, Dec 26 2024
2024-12-26T20:02:40
oeisdata/seq/A379/A379581.seq
011a444523efb572fb5f012cedf21caf
A379582
Denominators of the partial alternating sums of the reciprocals of the powerfree part function (A055231).
[ "1", "2", "6", "6", "30", "15", "105", "105", "105", "210", "2310", "2310", "30030", "15015", "1001", "1001", "17017", "34034", "646646", "3233230", "9699690", "4849845", "111546435", "37182145", "37182145", "74364290", "74364290", "74364290", "2156564410", "3234846615", "100280245065", "100280245065", "100280245065", "200560490130" ]
[ "nonn", "easy", "frac" ]
6
1
2
[ "A055231", "A370900", "A370901", "A379580", "A379581", "A379582" ]
null
Amiram Eldar, Dec 26 2024
2024-12-26T20:02:49
oeisdata/seq/A379/A379582.seq
7bec1916a7b7a65684f3b8f083d9dfdb
A379583
Numerators of the partial sums of the reciprocals of the powerful part function (A057521).
[ "1", "2", "3", "13", "17", "21", "25", "51", "467", "539", "611", "629", "701", "773", "845", "1699", "1843", "1859", "2003", "2039", "2183", "2327", "2471", "2489", "62369", "65969", "198307", "201007", "211807", "222607", "233407", "467489", "489089", "510689", "532289", "532889", "554489", "576089", "597689", "600389", "621989", "643589", "665189" ]
[ "nonn", "easy", "frac" ]
6
1
2
[ "A057521", "A191622", "A370902", "A370903", "A379583", "A379584", "A379585" ]
null
Amiram Eldar, Dec 26 2024
2024-12-26T20:02:58
oeisdata/seq/A379/A379583.seq
2fb686b621f21295614d5e7333f9061d
A379584
Denominators of the partial sums of the reciprocals of the powerful part function (A057521).
[ "1", "1", "1", "4", "4", "4", "4", "8", "72", "72", "72", "72", "72", "72", "72", "144", "144", "144", "144", "144", "144", "144", "144", "144", "3600", "3600", "10800", "10800", "10800", "10800", "10800", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "1058400" ]
[ "nonn", "easy", "frac" ]
6
1
4
[ "A057521", "A370902", "A370903", "A379583", "A379584", "A379586" ]
null
Amiram Eldar, Dec 26 2024
2024-12-26T20:03:05
oeisdata/seq/A379/A379584.seq
fd59ada46c8bbcf4d6ed00396cc0ef68
A379585
Numerators of the partial alternating sums of the reciprocals of the powerful part function (A057521).
[ "1", "0", "1", "3", "7", "3", "7", "13", "125", "53", "125", "107", "179", "107", "179", "349", "493", "53", "69", "65", "81", "65", "81", "79", "1991", "1591", "43357", "40657", "51457", "40657", "51457", "102239", "123839", "102239", "123839", "123239", "144839", "123239", "144839", "142139", "163739", "142139", "163739", "158339", "160739", "139139" ]
[ "nonn", "easy", "frac" ]
6
1
4
[ "A057521", "A191622", "A370902", "A370903", "A379583", "A379585", "A379586" ]
null
Amiram Eldar, Dec 26 2024
2024-12-26T20:03:13
oeisdata/seq/A379/A379585.seq
b6990e0455c207f5bfcdf1b9c76fdfff
A379586
Denominators of the partial alternating sums of the reciprocals of the powerful part function (A057521).
[ "1", "1", "1", "4", "4", "4", "4", "8", "72", "72", "72", "72", "72", "72", "72", "144", "144", "16", "16", "16", "16", "16", "16", "16", "400", "400", "10800", "10800", "10800", "10800", "10800", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "21600", "1058400" ]
[ "nonn", "easy", "frac" ]
6
1
4
[ "A057521", "A370902", "A370903", "A379584", "A379585", "A379586" ]
null
Amiram Eldar, Dec 26 2024
2024-12-26T20:03:20
oeisdata/seq/A379/A379586.seq
f8fddd84f8e6459555dd28a9e1937678
A379587
Array read by ascending antidiagonals: A(n, k) = (k^n - 1)^2/(k - 1), with k >= 2.
[ "0", "1", "0", "9", "2", "0", "49", "32", "3", "0", "225", "338", "75", "4", "0", "961", "3200", "1323", "144", "5", "0", "3969", "29282", "21675", "3844", "245", "6", "0", "16129", "264992", "348843", "97344", "9245", "384", "7", "0", "65025", "2389298", "5589675", "2439844", "335405", "19494", "567", "8", "0", "261121", "21516800", "89467563", "61027344", "12090125", "960000", "37303", "800", "9", "0" ]
[ "nonn", "easy", "tabl" ]
8
0
4
[ "A027620", "A060867", "A060868", "A060869", "A060870", "A060871", "A361475", "A379587", "A379588" ]
null
Stefano Spezia, Dec 26 2024
2024-12-26T20:01:43
oeisdata/seq/A379/A379587.seq
ca5ce638a91fc2e978036dec1e0a4383
A379588
Antidiagonal sums of the array A379587.
[ "0", "1", "11", "84", "642", "5633", "59021", "736944", "10839316", "185361065", "3637063343", "80939054884", "2023405966486", "56362728831929", "1736960568923505", "58853395571312176", "2180579093801111176", "87921539854223957169", "3841160785119756991059" ]
[ "nonn" ]
7
0
3
[ "A361476", "A379587", "A379588" ]
null
Stefano Spezia, Dec 26 2024
2024-12-26T20:01:52
oeisdata/seq/A379/A379588.seq
3e847a2ea1530d1886a83662b47f213c
A379589
Maximum number of connections for a 4 X n rectangle.
[ "1", "31", "800", "6466", "60778", "441492", "3216584", "18693320" ]
[ "nonn", "more" ]
7
2
2
[ "A379241", "A379393", "A379589" ]
null
Rodolfo Kurchan, Dec 26 2024
2024-12-26T19:58:56
oeisdata/seq/A379/A379589.seq
2feb5a0405c94daba39bb5314421d242
A379590
a(n) is the number of prime divisors d of n such that 2^d - 1 is prime.
[ "0", "1", "1", "1", "1", "2", "1", "1", "1", "2", "0", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "0", "2", "1", "2", "1", "2", "0", "3", "1", "1", "1", "2", "2", "2", "0", "2", "2", "2", "0", "3", "0", "1", "2", "1", "0", "2", "1", "2", "2", "2", "0", "2", "1", "2", "2", "1", "0", "3", "1", "2", "2", "1", "2", "2", "0", "2", "1", "3", "0", "2", "0", "1", "2", "2", "1", "3", "0", "2", "1", "1", "0", "3", "2", "1", "1", "1", "1", "3", "2", "1", "2", "1", "2", "2", "0", "2", "1", "2" ]
[ "nonn" ]
32
1
6
[ "A000005", "A000043", "A054723", "A379590" ]
null
Juri-Stepan Gerasimov, Dec 26 2024
2025-01-11T19:08:34
oeisdata/seq/A379/A379590.seq
cc4ec6a9b22dce2efa2097cb52949381
A379591
Numbers k whose base-10 digits can be split into two parts, q and r, with k = (|q-r|)^3.
[ "1000", "456533", "474552", "1000000", "69426531", "1000000000", "1000000000000", "1000000000000000", "1000000000000000000", "1000000000000000000000", "1000000000000000000000000", "1000000000000000000000000000", "1000000000000000000000000000000", "1000000000000000000000000000000000" ]
[ "nonn", "base" ]
17
1
1
[ "A102766", "A228103", "A379591" ]
null
Travis Vasquez, Dec 26 2024
2025-01-14T17:14:38
oeisdata/seq/A379/A379591.seq
5c1650195b5b6633c1611293b22e827d
A379592
Number of coreful divisor pairs (d, k/d), d | k, d < k/d, such that only one divisor divides the other, where k is in A320966.
[ "1", "1", "1", "2", "2", "1", "1", "1", "1", "3", "1", "1", "1", "2", "3", "2", "1", "1", "1", "1", "2", "1", "4", "2", "1", "2", "1", "2", "1", "2", "2", "1", "2", "1", "4", "1", "3", "3", "1", "1", "1", "1", "2", "2", "3", "1", "1", "2", "2", "1", "5", "3", "1", "3", "1", "1", "1", "4", "1", "1", "1", "1", "2", "1", "2", "2", "3", "1", "1", "3", "1", "1", "2", "4", "1", "2", "5", "1", "1", "1", "4", "1", "1", "2", "5", "1", "1" ]
[ "nonn" ]
6
1
4
[ "A320966", "A370329", "A379552", "A379592" ]
null
Michael De Vlieger, Dec 28 2024
2025-01-01T01:47:43
oeisdata/seq/A379/A379592.seq
fd8bc406b18c4b96c79c56cdc965b1ea
A379593
Numbers that set records in A379592.
[ "8", "32", "128", "512", "2048", "8192", "20736", "41472", "82944", "165888", "186624", "373248", "746496", "1492992", "2985984", "5971968", "6718464", "11943936", "23887872", "26873856", "53747712", "107495424", "214990848", "241864704", "429981696", "859963392", "967458816", "1719926784", "3439853568", "3869835264", "7464960000" ]
[ "nonn" ]
8
1
1
[ "A005934", "A025487", "A320966", "A361430", "A370329", "A379592", "A379593", "A379594" ]
null
Michael De Vlieger, Dec 30 2024
2025-01-01T01:47:54
oeisdata/seq/A379/A379593.seq
0a6394573011877e3e841d19f71f5fc8
A379594
Records in A379592.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "14", "15", "17", "18", "19", "20", "21", "23", "24", "27", "28", "29", "31", "32", "34", "35", "36", "39", "41", "44", "47", "48", "49", "53", "55", "59", "62", "63", "71", "72", "74", "83", "84", "89", "95", "96", "104", "107", "111", "119", "120", "125", "127", "134", "139", "143", "149", "159", "161", "167", "179", "180" ]
[ "nonn" ]
6
1
2
[ "A036965", "A379554", "A379592", "A379593", "A379594" ]
null
Michael De Vlieger, Dec 30 2024
2025-01-01T01:48:02
oeisdata/seq/A379/A379594.seq
cb663b4697c3434d57c1f1da99cb6416
A379595
Numbers k for which A376900(k) = k.
[ "0", "385", "386", "387", "390", "392", "404", "405", "406" ]
[ "nonn", "fini", "full" ]
4
1
2
[ "A376900", "A379595" ]
null
Felix Huber, Dec 26 2024
2025-01-07T10:21:33
oeisdata/seq/A379/A379595.seq
f73eeeb1feeaeefd4bd3dd35cb73493e
A379596
a(n) is the least positive integer k for which k^2 + (k + n)^2 is a square.
[ "3", "6", "9", "12", "15", "18", "5", "24", "27", "30", "33", "36", "39", "10", "45", "48", "7", "54", "57", "60", "15", "66", "12", "72", "75", "78", "81", "20", "87", "90", "9", "96", "99", "14", "25", "108", "111", "114", "117", "120", "36", "30", "129", "132", "135", "24", "16", "144", "11", "150", "21", "156", "159", "162", "165", "40", "171", "174", "177", "180", "183", "18", "45" ]
[ "nonn", "easy" ]
26
1
1
[ "A009004", "A089015", "A120682", "A132404", "A289398", "A379596", "A379830" ]
null
Felix Huber, Feb 15 2025
2025-03-02T10:02:12
oeisdata/seq/A379/A379596.seq
63a5125cc8d411655892246843e17b3b
A379597
a(n) is the number of distinct solution sets to the quadratic equations u*x^2 + v*x + w = 0 with integer coefficients u, v, w, abs(u) + abs(v) + abs(w) <= n having a nonnegative discriminant.
[ "1", "4", "12", "24", "50", "80", "134", "192", "276", "366", "510", "632", "834", "1018", "1262", "1502", "1858", "2136", "2584", "2956", "3448", "3910", "4576", "5076", "5834", "6488", "7320", "8066", "9136", "9892", "11118", "12114", "13358", "14482", "15978", "17108", "18862", "20272", "22024", "23532", "25700", "27216", "29600", "31486", "33746" ]
[ "nonn" ]
20
1
2
[ "A067274", "A091626", "A091627", "A364384", "A364385", "A365876", "A365877", "A379597", "A381710", "A381711" ]
null
Felix Huber, Feb 18 2025
2025-03-12T04:16:16
oeisdata/seq/A379/A379597.seq
8afd7c03c5dcae96b8109d45322725ce
A379598
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A110447.
[ "1", "1", "0", "1", "1", "0", "1", "2", "2", "0", "1", "3", "5", "6", "0", "1", "4", "9", "16", "23", "0", "1", "5", "14", "31", "62", "104", "0", "1", "6", "20", "52", "123", "278", "531", "0", "1", "7", "27", "80", "213", "552", "1398", "2982", "0", "1", "8", "35", "116", "340", "964", "2750", "7718", "18109", "0", "1", "9", "44", "161", "513", "1561", "4784", "14976", "46083", "117545", "0" ]
[ "nonn", "tabl" ]
19
0
8
[ "A000007", "A030266", "A110447", "A379598", "A379599", "A380178" ]
null
Seiichi Manyama, Feb 27 2025
2025-02-27T11:17:19
oeisdata/seq/A379/A379598.seq
4f7606e8280d59dff1b98d1a1fee60db
A379599
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A088714.
[ "1", "1", "0", "1", "1", "0", "1", "2", "3", "0", "1", "3", "7", "13", "0", "1", "4", "12", "32", "69", "0", "1", "5", "18", "58", "173", "419", "0", "1", "6", "25", "92", "321", "1054", "2809", "0", "1", "7", "33", "135", "523", "1971", "7039", "20353", "0", "1", "8", "42", "188", "790", "3248", "13158", "50632", "157199", "0", "1", "9", "52", "252", "1134", "4976", "21740", "94194", "387613", "1281993", "0" ]
[ "nonn", "tabl" ]
18
0
8
[ "A000007", "A088714", "A379168", "A379598", "A379599" ]
null
Seiichi Manyama, Feb 27 2025
2025-02-27T11:17:27
oeisdata/seq/A379/A379599.seq
5547a5ce4f955dba4c2aaaf8ec4e3136
A379600
a(n) is the semiperimeter of the primitive Pythagorean triangle (x(n), y(n), z(n)) with x(n) < y(n) < z(n) and x(n) > x(n-1), y(n) > y(n-1), z(n) > z(n-1), which has the smallest perimeter (if there are several triangles with smallest perimeter: the one of these with the smallest area), starting from a(1) = (3 + 4 + 5)/2 = 6.
[ "6", "15", "20", "35", "63", "77", "99", "104", "130", "165", "204", "247", "266", "336", "345", "391", "425", "450", "513", "580", "609", "651", "713", "805", "825", "888", "945", "1036", "1107", "1204", "1271", "1376", "1457", "1530", "1617", "1645", "1764", "1887", "1961", "2014", "2090", "2280", "2337", "2419", "2537", "2562", "2684", "2772", "2990", "3149" ]
[ "nonn" ]
34
1
1
[ "A010814", "A020886", "A118858", "A379600" ]
null
Felix Huber, Feb 15 2025
2025-03-05T18:59:59
oeisdata/seq/A379/A379600.seq
a705d7598c707af2cb98c1dc54dc901c
A379601
Decimal expansion of (120e^6 - 600e^5 + 960e^4 - 540e^3 + 80e^2 - e) / 120.
[ "1", "2", "6", "6", "6", "6", "6", "7", "1", "4", "1", "3", "7", "8", "1", "2", "1", "4", "0", "1", "3", "7", "1", "9", "3", "5", "7", "6", "2", "6", "8", "4", "9", "1", "1", "1", "9", "5", "6", "4", "7", "4", "3", "7", "0", "7", "7", "7", "4", "0", "1", "9", "6", "7", "5", "6", "7", "1", "0", "5", "3", "7", "5", "5", "6", "8", "2", "6", "0", "2", "8", "7", "6", "9", "4", "0", "6", "7", "8", "4", "2", "4", "8", "7", "0", "0", "5", "6", "0", "0", "9", "8", "0", "3", "5", "2", "2", "4", "0", "2", "0", "7", "8", "0", "7", "5", "9", "7", "6", "1", "6" ]
[ "nonn", "cons", "easy" ]
33
2
2
[ "A001113", "A089087", "A089139", "A090142", "A090143", "A090611", "A379601", "A381673" ]
null
Daniel Mondot, Feb 27 2025
2025-03-23T08:40:06
oeisdata/seq/A379/A379601.seq
8e9619b50707d88ad5aac1a6e8fa9c2e