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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
A380806
Numbers not of form a*(b+1) + b*(c+1) + c*(a+1) for 1<=a<=b<=c.
[ "1", "2", "3", "4", "5", "7", "8", "10", "11", "14", "16", "19", "20", "26", "31", "34", "40", "44", "55", "76", "80", "94", "124", "160", "170", "220", "271" ]
[ "nonn", "more" ]
9
1
2
[ "A025052", "A380806", "A380807" ]
null
Seiichi Manyama, Feb 04 2025
2025-02-04T14:45:21
oeisdata/seq/A380/A380806.seq
298fd0afe81edef7e509b388b9d6518a
A380807
Numbers not of form a*(b+1) + b*(c+1) + c*(a+1) for 0<a<b<c.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "18", "19", "20", "22", "23", "24", "26", "28", "30", "31", "34", "36", "38", "40", "43", "44", "46", "48", "50", "54", "55", "58", "64", "66", "68", "76", "78", "79", "80", "90", "94", "100", "106", "108", "118", "120", "124", "134", "138", "148", "156", "160", "170", "178", "198", "220", "271", "274", "288", "358", "376", "498", "750", "828" ]
[ "nonn" ]
6
1
2
[ "A000926", "A380806", "A380807" ]
null
Seiichi Manyama, Feb 04 2025
2025-02-04T09:34:35
oeisdata/seq/A380/A380807.seq
1a9854d9ae76235ef46f2736491d151c
A380808
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x) / (1 + x*exp(-x)) ).
[ "1", "3", "24", "335", "6812", "183397", "6168406", "249350285", "11785793352", "638146503593", "38960123581154", "2648475653518081", "198429466488527164", "16246940820392924189", "1443430758561178861758", "138305198841617791230533", "14217431594874334746229520", "1560842183273111251153540945" ]
[ "nonn" ]
27
0
2
[ "A088690", "A161633", "A352448", "A380808", "A380826", "A380828" ]
null
Seiichi Manyama, Feb 04 2025
2025-02-05T09:23:43
oeisdata/seq/A380/A380808.seq
909a5359c73b14431f4891573f5e6be5
A380809
For n a power of 2, a(n) = n. If n is not a power of 2, a(n) is the smallest number not yet in the sequence which shares a decimal digit and a prime factor with n, and has the same binary weight.
[ "1", "2", "33", "4", "65", "36", "70", "8", "96", "12", "176", "10", "104", "21", "45", "16", "136", "48", "133", "24", "14", "26", "92", "20", "35", "22", "57", "38", "232", "39", "93", "32", "3", "40", "25", "6", "74", "28", "30", "34", "164", "44", "344", "42", "15", "54", "94", "18", "84", "52", "75", "50", "3392", "46", "115", "76", "27", "78", "295", "86", "122", "124", "123", "64" ]
[ "nonn", "base" ]
14
1
2
[ "A000120", "A380809" ]
null
David James Sycamore, Feb 04 2025
2025-02-23T11:17:15
oeisdata/seq/A380/A380809.seq
f87f24595f2212eb3efc4b2ee657c48b
A380810
Integers m for which m = Sum (d_i - 1)^k, where m is k decimal digits long and d_i are the digits of m.
[ "26", "126", "217", "729", "4193", "134068", "10875747", "24228197", "2491591748", "106557756999043" ]
[ "nonn", "base", "fini", "full" ]
32
1
1
[ "A005188", "A261433", "A380810" ]
null
Paolo P. Lava, Feb 04 2025
2025-02-05T22:17:03
oeisdata/seq/A380/A380810.seq
475130ace9cd3a400527c54e7ed55ec1
A380811
Smallest composite number divisible by prime(n) which shares at least one decimal digit with prime(n).
[ "12", "30", "15", "70", "110", "39", "51", "95", "92", "203", "93", "74", "123", "301", "94", "159", "295", "122", "268", "142", "365", "237", "332", "178", "194", "202", "206", "214", "218", "339", "254", "393", "274", "417", "298", "453", "314", "326", "501", "346", "537", "1086", "955", "386", "394", "398", "422", "892", "1362", "916", "932", "956", "482", "502", "514" ]
[ "nonn", "base" ]
18
1
1
[ "A000040", "A380811" ]
null
David James Sycamore, Feb 04 2025
2025-02-05T22:14:04
oeisdata/seq/A380/A380811.seq
64b15f04ee091eef3266332822814e28
A380812
Sequence of x-coordinates of the lexicographically earliest (according to the spiral numbering of the square grid; see comments) infinite Racetrack trajectory (using von Neumann neighborhood) on the square grid.
[ "0", "1", "2", "2", "1", "0", "-1", "-1", "-1", "-1", "0", "1", "2", "2", "2", "1", "0", "-1", "-2", "-3", "-3", "-2", "-1", "0", "1", "3", "4", "4", "4", "3", "2", "1", "-1", "-3", "-4", "-4", "-4", "-4", "-3", "-2", "0", "2", "4", "5", "5", "4", "3", "2", "0", "-2", "-4", "-5", "-5", "-5", "-5", "-4", "-3", "-1", "1", "3", "4", "4", "3", "2", "1", "-1", "-3", "-5", "-6", "-6", "-5", "-3", "0", "3", "6", "8" ]
[ "sign" ]
10
0
3
[ "A174344", "A316328", "A351042", "A351043", "A380812", "A380813", "A380814" ]
null
Pontus von Brömssen, Feb 05 2025
2025-02-05T16:18:47
oeisdata/seq/A380/A380812.seq
900516154994d4d9f13b3bb7d3055f83
A380813
Sequence of y-coordinates of the lexicographically earliest (according to the spiral numbering of the square grid; see comments) infinite Racetrack trajectory (using von Neumann neighborhood) on the square grid.
[ "0", "0", "-1", "-2", "-3", "-3", "-2", "-1", "1", "2", "3", "3", "2", "1", "0", "-1", "-1", "0", "2", "3", "4", "5", "5", "4", "2", "0", "-2", "-4", "-5", "-6", "-6", "-5", "-4", "-2", "0", "2", "4", "5", "6", "6", "6", "5", "3", "1", "-1", "-3", "-4", "-4", "-4", "-3", "-1", "1", "3", "5", "6", "7", "7", "7", "6", "4", "2", "0", "-2", "-3", "-4", "-5", "-5", "-4", "-3", "-2", "-1", "0", "1", "1", "0", "-1" ]
[ "sign" ]
5
0
4
[ "A274923", "A351042", "A351043", "A380812", "A380813", "A380814" ]
null
Pontus von Brömssen, Feb 05 2025
2025-02-05T14:31:10
oeisdata/seq/A380/A380813.seq
d834414e50048fe110b73b9ff288a12e
A380814
Squared distance to the origin after the n-th step of the Racetrack trajectory in A380812 and A380813.
[ "0", "1", "5", "8", "10", "9", "5", "2", "2", "5", "9", "10", "8", "5", "4", "2", "1", "1", "8", "18", "25", "29", "26", "16", "5", "9", "20", "32", "41", "45", "40", "26", "17", "13", "16", "20", "32", "41", "45", "40", "36", "29", "25", "26", "26", "25", "25", "20", "16", "13", "17", "26", "34", "50", "61", "65", "58", "50", "37", "25", "20", "16", "13", "13", "17", "26", "34", "41", "45", "40" ]
[ "nonn" ]
5
0
3
[ "A380812", "A380813", "A380814" ]
null
Pontus von Brömssen, Feb 05 2025
2025-02-05T14:31:19
oeisdata/seq/A380/A380814.seq
e3e69be7d56cdd32abc2ba587196fd90
A380815
a(n) = A378684(A379343(n)).
[ "1", "5", "2", "4", "3", "6", "12", "9", "14", "7", "11", "10", "13", "8", "15", "23", "20", "25", "18", "27", "16", "22", "21", "24", "19", "26", "17", "28", "38", "35", "40", "33", "42", "31", "44", "29", "37", "36", "39", "34", "41", "32", "43", "30", "45", "57", "54", "59", "52", "61", "50", "63", "48", "65", "46", "56", "55", "58", "53", "60", "51", "62", "49", "64", "47", "66" ]
[ "nonn", "tabf" ]
24
1
2
[ "A000027", "A000384", "A016813", "A376214", "A378684", "A379342", "A379343", "A380200", "A380245", "A380815", "A380817", "A381662", "A381663", "A381664" ]
null
Boris Putievskiy, Feb 04 2025
2025-04-09T22:52:16
oeisdata/seq/A380/A380815.seq
255aea0e7f5300aa9d09da833975f92a
A380816
Number of pairs (x, y) with 0 < x < y < n such that x^y = y^x modulo n.
[ "0", "0", "0", "0", "1", "1", "5", "2", "2", "3", "5", "6", "8", "8", "6", "18", "11", "7", "20", "16", "15", "17", "28", "28", "15", "23", "32", "27", "24", "22", "35", "88", "20", "31", "19", "34", "32", "43", "35", "72", "33", "40", "37", "52", "45", "51", "57", "134", "36", "37", "38", "73", "65", "73", "61", "118", "72", "52", "59", "94", "61", "74", "111", "428", "67", "65", "69" ]
[ "nonn", "nice" ]
25
1
7
null
null
Peter Schorn, Feb 04 2025
2025-03-17T11:31:01
oeisdata/seq/A380/A380816.seq
3f21a2846b9843f74352fc4b946204f0
A380817
a(n) = A380245(A379343(n)).
[ "1", "2", "3", "4", "5", "6", "9", "10", "7", "8", "11", "12", "13", "14", "15", "20", "21", "18", "19", "16", "17", "22", "23", "24", "25", "26", "27", "28", "35", "36", "33", "34", "31", "32", "29", "30", "37", "38", "39", "40", "41", "42", "43", "44", "45", "54", "55", "52", "53", "50", "51", "48", "49", "46", "47", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66" ]
[ "nonn", "tabf", "changed" ]
29
1
2
[ "A000027", "A000384", "A016813", "A376214", "A378684", "A379342", "A379343", "A380200", "A380245", "A380815", "A380817", "A381662", "A381663", "A381664", "A381968", "A382499", "A382679", "A382680" ]
null
Boris Putievskiy, Feb 04 2025
2025-04-24T18:37:40
oeisdata/seq/A380/A380817.seq
527b7b16eac09fb50a56d354ae99e4ed
A380818
Numbers k such that the Diophantine equation d_r*x^r + ... + d_0*x^0 = 0 has an integer solution. k = (d_r .. d_0) in decimal notation, d_i are the digits of k.
[ "0", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "22", "24", "26", "28", "30", "33", "36", "39", "40", "44", "48", "50", "55", "60", "66", "70", "77", "80", "88", "90", "99", "100", "110", "120", "121", "130", "132", "140", "143", "144", "150", "154", "156", "160", "165", "168", "169", "170", "176", "180", "187", "190", "198", "200", "210", "220", "230", "231", "240", "242", "250" ]
[ "nonn", "base" ]
11
1
2
[ "A037124", "A380818" ]
null
Ctibor O. Zizka, Feb 04 2025
2025-02-05T22:09:03
oeisdata/seq/A380/A380818.seq
684f0bdaedaa15f2cced21584a2934ce
A380819
Triangle read by rows where row n lists "weak" divisors d | n (i.e., d in A052485) such that rad(d)^2 does not divide d, where rad = A007947.
[ "2", "3", "2", "5", "2", "3", "6", "7", "2", "3", "2", "5", "10", "11", "2", "3", "6", "12", "13", "2", "7", "14", "3", "5", "15", "2", "17", "2", "3", "6", "18", "19", "2", "5", "10", "20", "3", "7", "21", "2", "11", "22", "23", "2", "3", "6", "12", "24", "5", "2", "13", "26", "3", "2", "7", "14", "28", "29", "2", "3", "5", "6", "10", "15", "30", "31", "2", "3", "11", "33", "2", "17", "34", "5", "7", "35", "2", "3", "6", "12", "18" ]
[ "nonn", "tabf", "easy" ]
7
2
1
[ "A000005", "A001694", "A005361", "A007947", "A027750", "A052485", "A183093", "A379545", "A380672", "A380819" ]
null
Michael De Vlieger, Feb 13 2025
2025-02-16T23:02:26
oeisdata/seq/A380/A380819.seq
f9d71a5a0bbf1d2c52dc34d28b0d327c
A380820
a(0) = 0, a(1) = 1, and for n >= 2, a(n) = a(n-1) + a(n-2) if a(n-1) < n, otherwise a(n-1) - n.
[ "0", "1", "1", "2", "3", "5", "8", "1", "9", "0", "9", "9", "18", "5", "23", "8", "31", "14", "45", "26", "6", "32", "10", "42", "18", "60", "34", "7", "41", "12", "53", "22", "75", "42", "8", "50", "14", "64", "26", "90", "50", "9", "59", "16", "75", "30", "105", "58", "10", "68", "18", "86", "34", "120", "66", "11", "77", "20", "97", "38", "135", "74", "12", "86", "22", "108", "42", "150" ]
[ "nonn", "easy" ]
19
0
4
[ "A000027", "A000045", "A005843", "A008597", "A016825", "A017089", "A017221", "A017497", "A322558", "A380820" ]
null
Ya-Ping Lu, Feb 04 2025
2025-02-14T23:11:09
oeisdata/seq/A380/A380820.seq
dca51d72e76aba29b55e6a1b485124b0
A380821
Table read by rows: row n is the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
[ "5", "12", "13", "3", "4", "5", "7", "24", "25", "9", "40", "41", "15", "112", "113", "23", "264", "265", "37", "684", "685", "59", "1740", "1741", "95", "4512", "4513", "153", "11704", "11705", "247", "30504", "30505", "399", "79600", "79601", "645", "208012", "208013", "1043", "543924", "543925", "1687", "1422984", "1422985", "2729", "3723720", "3723721" ]
[ "nonn", "easy", "tabf" ]
17
0
1
[ "A000032", "A380821", "A380823", "A380824" ]
null
Miguel-Ángel Pérez García-Ortega, Feb 04 2025
2025-03-04T22:45:16
oeisdata/seq/A380/A380821.seq
e3a735813f581be215dc2ffd529c5f45
A380823
Semiperimeter of the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
[ "15", "6", "28", "45", "120", "276", "703", "1770", "4560", "11781", "30628", "79800", "208335", "544446", "1423828", "3725085", "9748320", "25514796", "66787903", "174835650", "457697640", "1198222581", "3136914028", "8212428720", "21500225295", "56288009526", "147363418828", "385801624845", "1010040449160", "2644318093956", "6922911197503" ]
[ "nonn", "easy" ]
29
0
1
[ "A000032", "A380821", "A380823", "A380824", "A381721" ]
null
Miguel-Ángel Pérez García-Ortega, Feb 04 2025
2025-03-21T02:24:05
oeisdata/seq/A380/A380823.seq
6da485e0c4089ec8a64319ca60639d84
A380824
Area of the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
[ "30", "6", "84", "180", "840", "3036", "12654", "51330", "214320", "895356", "3767244", "15880200", "67083870", "283656366", "1200287004", "5081015940", "21514542240", "91113336516", "385900503534", "1634538491850", "6923592200280", "29327695892556", "124231206250884", "526244219948880", "2229186359036190", "9442932766091286" ]
[ "nonn", "easy" ]
20
0
1
[ "A000032", "A380821", "A380823", "A380824", "A381721" ]
null
Miguel-Ángel Pérez García-Ortega, Feb 04 2025
2025-03-14T21:30:53
oeisdata/seq/A380/A380824.seq
1b6ae5b4328b54fea5ca3159c426c93b
A380825
Indices of triangular numbers that are the products of triangular numbers larger than 1.
[ "8", "9", "20", "24", "27", "35", "39", "44", "54", "55", "75", "80", "84", "90", "98", "99", "104", "132", "135", "153", "175", "189", "195", "207", "224", "230", "231", "252", "260", "272", "275", "279", "285", "296", "324", "350", "351", "374", "399", "405", "440", "455", "459", "475", "494", "539", "560", "567", "575", "594", "615", "620", "624", "665", "675" ]
[ "nonn" ]
15
1
1
[ "A000217", "A003056", "A068143", "A380825" ]
null
Kelvin Voskuijl, Feb 04 2025
2025-02-13T12:20:58
oeisdata/seq/A380/A380825.seq
d0b6ac1c3bd660a7dd68a0631bcd12a3
A380826
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x) / (1 + x*exp(-2*x)) ).
[ "1", "4", "43", "810", "22273", "811728", "36979467", "2025462736", "129748802401", "9522843081984", "788169731306059", "72641846664240384", "7379343546762675873", "819269203286474309632", "98698960328223628470379", "12824232015954542746048512", "1787731339345567827140060737", "266157254062414638948185210880" ]
[ "nonn" ]
14
0
2
[ "A088690", "A161633", "A361182", "A380808", "A380826", "A380829", "A380830" ]
null
Seiichi Manyama, Feb 04 2025
2025-02-05T09:22:58
oeisdata/seq/A380/A380826.seq
65f240fce85e8a7af69575d1fe4a04f5
A380827
Least integer k such that the multiplicative group modulo n is a subgroup of the symmetric group S_k.
[ "1", "1", "2", "2", "4", "2", "5", "4", "5", "4", "7", "4", "7", "5", "6", "6", "16", "5", "11", "6", "7", "7", "13", "6", "9", "7", "11", "7", "11", "6", "10", "10", "9", "16", "9", "7", "13", "11", "9", "8", "13", "7", "12", "9", "9", "13", "25", "8", "12", "9", "18", "9", "17", "11", "11", "9", "13", "11", "31", "8", "12", "10", "10", "18", "11", "9", "16", "18", "15", "9", "14", "9", "17", "13", "11", "13", "12", "9", "18", "10", "29" ]
[ "nonn" ]
24
1
3
[ "A008475", "A282625", "A380222", "A380827" ]
null
Asher Gray, Feb 04 2025
2025-02-23T11:32:17
oeisdata/seq/A380/A380827.seq
3b66e928bf7d6ce06d31fc1a2da4c46e
A380828
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x) / (1 + x) ).
[ "1", "3", "26", "398", "8904", "264072", "9790192", "436382256", "22748241024", "1358633214080", "91503397265664", "6862436244211968", "567252637423922176", "51244493078278198272", "5023312927780022323200", "531082672018567209801728", "60239691905397303186849792", "7297357396264290237329473536" ]
[ "nonn" ]
12
0
2
[ "A088690", "A352448", "A376093", "A380808", "A380828", "A380830" ]
null
Seiichi Manyama, Feb 05 2025
2025-02-05T09:23:40
oeisdata/seq/A380/A380828.seq
6c00d13666a3b2f791138cbab36c34da
A380829
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x) / (1 + x*exp(-x)) ).
[ "1", "4", "45", "891", "25757", "986653", "47235873", "2718521725", "182963698521", "14107443728553", "1226582182222469", "118751669770995913", "12671598073554789909", "1477709279563430592877", "186988047586389278202633", "25518989446806209718773157", "3736444151435292273253963313", "584269287631534621583659461841" ]
[ "nonn" ]
9
0
2
[ "A361182", "A380826", "A380829", "A380830" ]
null
Seiichi Manyama, Feb 05 2025
2025-02-05T09:23:02
oeisdata/seq/A380/A380829.seq
eaebf49891e65bee5d0151d957d69204
A380830
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x) / (1 + x) ).
[ "1", "4", "47", "978", "29769", "1201728", "60656679", "3681441648", "261337079601", "21256149703680", "1949700750690879", "199146039242552064", "22420399033075845177", "2758645779752490872832", "368321963942753147683575", "53038788218443786432223232", "8194316429830951008255159009", "1352065789150879084276947222528" ]
[ "nonn" ]
12
0
2
[ "A088690", "A361182", "A376094", "A380826", "A380828", "A380829", "A380830" ]
null
Seiichi Manyama, Feb 05 2025
2025-02-05T09:23:06
oeisdata/seq/A380/A380830.seq
f4820c5ea0567e3067ada27b0a5336c1
A380831
Numbers k such that k^(k + 1) == k + 1 (mod 2*k + 1) while 2*k+1 is not prime.
[ "1023", "1638", "14670", "21399", "24570", "40290", "44178", "45375", "52326", "98046", "128499", "135975", "157410", "229494", "244998", "257223", "370875", "400302", "419430", "436590", "458163", "502326", "625974", "686826", "754854", "839270", "905786", "993510", "1102983", "1134546", "1142226", "1152083", "1193898", "1373238", "1374011" ]
[ "nonn" ]
5
1
1
[ "A047845", "A374913", "A380831" ]
null
Michel Marcus, Feb 05 2025
2025-02-05T09:02:50
oeisdata/seq/A380/A380831.seq
7d337174821493e93f58d24b1fd24f70
A380832
Number of points in Z^4 of norm <= n where the sum of the four entries is even.
[ "1", "1", "49", "169", "625", "1465", "3337", "5689", "10009", "15937", "24865", "35761", "51265", "69817", "94849", "124009", "161497", "204529", "260137", "320497", "394705", "478705", "577489", "687913", "819313", "960457", "1127785", "1309153", "1517161", "1742497", "2001505", "2273473", "2585905", "2920009", "3297337", "3700153", "4144105", "4618657", "5145865", "5703073" ]
[ "nonn" ]
17
0
3
[ "A055410", "A380832" ]
null
Steven Lu, Feb 05 2025
2025-02-12T14:22:37
oeisdata/seq/A380/A380832.seq
38049a4503f69bccc8d5504333d1ae28
A380833
a(n) is the number of divisors d of n satisfying (-d)^n mod n = d.
[ "0", "1", "0", "1", "0", "2", "0", "1", "0", "2", "0", "2", "0", "2", "1", "1", "0", "2", "0", "2", "0", "2", "0", "1", "0", "2", "0", "2", "0", "4", "0", "1", "0", "2", "1", "2", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "2", "0", "2", "0", "2", "0", "2", "0", "2", "0", "2", "0", "1", "0", "2", "0", "1", "0", "4", "0", "2", "0", "2", "0", "2", "0", "2", "0", "1", "0", "3", "0", "2", "0", "2", "0", "3", "0", "2", "0", "1", "0", "3", "1", "1", "0", "2", "0", "1", "0", "2", "0", "2" ]
[ "nonn" ]
18
1
6
[ "A000005", "A371883", "A380656", "A380833" ]
null
Juri-Stepan Gerasimov, Feb 06 2025
2025-02-06T12:28:35
oeisdata/seq/A380/A380833.seq
5f53a767cff1d5848542d3badf468695
A380834
First column of Kimberling's ESC array.
[ "1", "4", "7", "9", "11", "15", "17", "20", "22", "25", "27", "30", "33", "35", "38", "41", "43", "46", "49", "51", "53", "57", "59", "61", "64", "67", "69", "72", "75", "77", "79", "83", "85", "88", "90", "93", "95", "99", "101", "103", "106", "109", "111", "114", "117", "119", "121", "125", "127", "130", "132", "135", "137", "140", "143", "145", "148", "151", "153", "156" ]
[ "nonn" ]
19
1
2
[ "A380834", "A380835" ]
null
Jeffrey Shallit, Feb 05 2025
2025-02-06T09:26:02
oeisdata/seq/A380/A380834.seq
676278f936fec7f820df89796fa292b5
A380835
Second column of Kimberling's ESC array.
[ "2", "6", "12", "14", "18", "24", "28", "32", "36", "40", "44", "48", "54", "56", "62", "66", "70", "74", "80", "82", "86", "92", "96", "98", "104", "108", "112", "116", "122", "124", "128", "134", "138", "142", "146", "150", "154", "160", "164", "166", "172", "176", "180", "184", "190", "192", "196", "202", "206", "210", "214", "218", "222", "226", "232", "234", "240" ]
[ "nonn" ]
18
1
1
[ "A380834", "A380835" ]
null
Jeffrey Shallit, Feb 05 2025
2025-02-06T09:26:04
oeisdata/seq/A380/A380835.seq
b22830dbe1fdc7904fe8d7d07e0a1f4c
A380836
a(n) is the smallest k such that tau(2*k) is equal to 2^n, where tau = A000005.
[ "1", "3", "12", "60", "420", "3780", "41580", "540540", "8648640", "147026880", "2793510720", "64250746560", "1606268664000", "46581791256000", "1444035528936000", "53429314570632000", "2190601897395912000", "94195881588024216000", "4427206434637138152000", "216933115297219769448000", "11497455110752647780744000" ]
[ "nonn" ]
43
1
2
[ "A000005", "A000028", "A005843", "A037992", "A099777", "A380836" ]
null
Juri-Stepan Gerasimov, Feb 06 2025
2025-02-16T22:30:38
oeisdata/seq/A380/A380836.seq
da62a69db01aed02794139311c9e3834
A380837
Sequence Sg of the eight sequences defining the blocks of terms in A377091.
[ "4", "9", "20", "31", "42", "60", "81", "100", "121", "147", "183", "210", "241", "272", "307", "342", "400", "441", "484", "529", "576", "651", "703", "757", "813", "871", "931", "965", "1023", "1059", "1089", "1125", "1190", "1228", "1296", "1369", "1408", "1448", "1520", "1525", "1598", "1603", "1681", "1764", "1849", "1936", "2070", "2117", "2209", "2302" ]
[ "nonn" ]
7
1
1
[ "A377091", "A379066", "A379788", "A379789", "A379790", "A379791", "A379792", "A379793", "A379794", "A380837", "A380838" ]
null
Paolo Xausa, Feb 05 2025
2025-02-05T14:32:23
oeisdata/seq/A380/A380837.seq
33c38444d38f4edc02bd2d2b57cde471
A380838
Values of terms in A380837 which are not in A379066.
[ "965", "1089", "1228", "1448", "1525", "1603", "2117", "2307", "2404", "2916", "8650", "8837", "12544", "12999", "13458", "14402", "17690", "17957", "20737", "39205", "50177", "54292", "55699", "60518", "64517", "65028", "66053", "70757", "71827", "72364", "75077", "80657", "82947", "83524", "85852", "104977", "133957", "135427", "136164", "141377" ]
[ "nonn" ]
6
1
1
[ "A377091", "A379066", "A380837", "A380838" ]
null
Paolo Xausa, Feb 05 2025.
2025-02-05T14:47:37
oeisdata/seq/A380/A380838.seq
7a8e7c2d9d5492efa0c1568615149472
A380839
Numerators of J(n) = Product_{p|n, p odd prime} (p - 1)/(p - 2).
[ "1", "1", "2", "1", "4", "2", "6", "1", "2", "4", "10", "2", "12", "6", "8", "1", "16", "2", "18", "4", "12", "10", "22", "2", "4", "12", "2", "6", "28", "8", "30", "1", "20", "16", "8", "2", "36", "18", "24", "4", "40", "12", "42", "10", "8", "22", "46", "2", "6", "4", "32", "12", "52", "2", "40", "6", "36", "28", "58", "8", "60", "30", "12", "1", "16", "20", "66", "16", "44", "8", "70", "2", "72", "36" ]
[ "nonn", "frac" ]
37
1
3
[ "A167864", "A173557", "A305444", "A307410", "A380839" ]
null
Artur Jasinski, Feb 05 2025
2025-03-03T13:27:06
oeisdata/seq/A380/A380839.seq
25b33028f107573c6a419bb8bebb8d83
A380840
Decimal expansion of Sum_{p prime} 1/(p-1)^3.
[ "1", "1", "4", "7", "5", "2", "9", "0", "9", "7", "7", "5", "8", "5", "8", "0", "0", "4", "6", "9", "3", "3", "2", "8", "3", "8", "0", "6", "2", "8", "2", "1", "3", "0", "4", "0", "1", "6", "4", "4", "7", "6", "4", "7", "3", "5", "5", "2", "5", "1", "1", "2", "2", "5", "5", "2", "7", "5", "8", "2", "4", "1", "2", "3", "9", "5", "0", "5", "3", "3", "5", "9", "0", "4", "5", "5", "0", "4", "5", "4", "3", "1", "4", "7", "2", "6", "5", "2", "2", "8", "7", "3", "7", "2", "6", "9", "0", "9", "4", "6", "7", "5", "1", "6", "8", "0" ]
[ "nonn" ]
14
1
3
[ "A085541", "A085548", "A086242", "A136141", "A152441", "A154945", "A179119", "A324833", "A369632", "A380840" ]
null
Artur Jasinski, Mar 19 2025
2025-03-31T13:40:01
oeisdata/seq/A380/A380840.seq
5d868927ba7efb489ae58dd3ae2c69ae
A380841
Array read by ascending antidiagonals: A(n,k) = n! * [x^n] 1/(1 - x*exp(x))^k.
[ "1", "0", "1", "0", "1", "1", "0", "4", "2", "1", "0", "21", "10", "3", "1", "0", "148", "66", "18", "4", "1", "0", "1305", "560", "141", "28", "5", "1", "0", "13806", "5770", "1380", "252", "40", "6", "1", "0", "170401", "69852", "16095", "2776", "405", "54", "7", "1", "0", "2403640", "970886", "217458", "35940", "4940", "606", "70", "8", "1", "0", "38143377", "15228880", "3335745", "533304", "70045", "8088", "861", "88", "9", "1" ]
[ "nonn", "tabl" ]
15
0
8
[ "A000007", "A000012", "A001477", "A006153", "A028552", "A213643", "A377529", "A377530", "A379993", "A380841", "A380842", "A380843" ]
null
Stefano Spezia, Feb 05 2025
2025-02-06T10:23:26
oeisdata/seq/A380/A380841.seq
1e53b009ff01fd6d845a2a68c9b483c8
A380842
Main diagonal of the array A380841.
[ "1", "1", "10", "141", "2776", "70045", "2157156", "78452521", "3290644288", "156380715801", "8304267312100", "487328231729581", "31318669850761008", "2187567259278425557", "165011952533314548676", "13368463736048341225425", "1157693100510102752463616", "106719312722496774534400177", "10433609651067618426072766020" ]
[ "nonn" ]
12
0
3
[ "A213643", "A380841", "A380842" ]
null
Stefano Spezia, Feb 05 2025
2025-02-06T09:41:38
oeisdata/seq/A380/A380842.seq
67076220b1efa40c8e8f69a94715637d
A380843
Antidiagonal sums of the array A380841.
[ "1", "1", "2", "7", "35", "237", "2040", "21255", "259591", "3633549", "57320398", "1005959831", "19436938571", "409965565469", "9372278051700", "230832086585495", "6093185704307967", "171604903098322813", "5136091192685429770", "162792009969153667111", "5447239135976543715731", "191888373741260775025741" ]
[ "nonn" ]
4
0
3
[ "A380841", "A380843" ]
null
Stefano Spezia, Feb 05 2025
2025-02-05T22:05:16
oeisdata/seq/A380/A380843.seq
457f7cddc795c6ddd804a239f53af709
A380844
The number of divisors of n that have the same binary weight as n.
[ "1", "2", "1", "3", "1", "2", "1", "4", "2", "2", "1", "3", "1", "2", "1", "5", "1", "4", "1", "3", "2", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "6", "2", "2", "2", "6", "1", "2", "1", "4", "1", "4", "1", "3", "2", "2", "1", "5", "2", "2", "1", "3", "1", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "7", "2", "4", "1", "3", "1", "4", "1", "8", "1", "2", "2", "3", "1", "2", "1", "5", "1", "2", "1", "6", "1", "2", "1" ]
[ "nonn", "base", "easy" ]
10
1
2
[ "A000005", "A000043", "A000120", "A000265", "A000396", "A007814", "A324392", "A325565", "A380844", "A380845" ]
null
Amiram Eldar, Feb 05 2025
2025-02-07T00:43:46
oeisdata/seq/A380/A380844.seq
2c59b13fbe56e9a8b20191710ef76fc4
A380845
The sum of divisors of n that have the same binary weight as n.
[ "1", "3", "3", "7", "5", "9", "7", "15", "12", "15", "11", "21", "13", "21", "15", "31", "17", "36", "19", "35", "28", "33", "23", "45", "25", "39", "27", "49", "29", "45", "31", "63", "36", "51", "42", "84", "37", "57", "39", "75", "41", "84", "43", "77", "60", "69", "47", "93", "56", "75", "51", "91", "53", "81", "55", "105", "57", "87", "59", "105", "61", "93", "63", "127", "70", "108" ]
[ "nonn", "base", "easy" ]
10
1
2
[ "A000120", "A000203", "A000265", "A000396", "A000668", "A007814", "A038712", "A380844", "A380845" ]
null
Amiram Eldar, Feb 05 2025
2025-02-07T00:43:53
oeisdata/seq/A380/A380845.seq
4bf5caf389f326bdf13f7b4ccf47b470
A380846
Numbers k such that A380845(k) = 2*k.
[ "18", "42", "90", "186", "196", "306", "378", "420", "534", "618", "654", "690", "762", "834", "868", "906", "1062", "1110", "1194", "1242", "1326", "1362", "1422", "1458", "1530", "1698", "1764", "1818", "1866", "2118", "2214", "2262", "2324", "2346", "2490", "2598", "2670", "2706", "2730", "2778", "2838", "2862", "2884", "2922", "2958", "2994", "3066", "3138" ]
[ "nonn", "base", "easy" ]
14
1
1
[ "A000203", "A000396", "A005100", "A005101", "A380845", "A380846", "A380847", "A380848" ]
null
Amiram Eldar, Feb 05 2025
2025-02-10T16:10:06
oeisdata/seq/A380/A380846.seq
1a196f523dcf8b9baf757aa8774aa049
A380847
Numbers k such that A380845(k) = 3*k.
[ "1800", "3720", "7560", "15240", "20832", "30600", "42336", "61320", "85344", "109320", "116040", "122760", "171360", "218760", "238920", "245640", "343392", "346440", "395880", "437640", "462600", "484680", "491400", "580680", "687456", "854760", "875400", "896520", "917880", "925320", "950520", "954120", "976200", "982920", "1011720" ]
[ "nonn", "base", "easy" ]
11
1
1
[ "A000203", "A005100", "A005820", "A068403", "A380845", "A380846", "A380847", "A380848" ]
null
Amiram Eldar, Feb 05 2025
2025-02-09T06:54:15
oeisdata/seq/A380/A380847.seq
320936cd694e0dd5995ff52a519c1f89
A380848
Numbers k such that A380845(k) = 4*k.
[ "123832800", "247695840", "268337160", "495421920", "536707080", "990874080", "1073446920", "1981778400", "2146926600", "3963587040", "4293885960", "7927204320", "8587804680", "15854438880", "17175642120", "31708908000", "34351317000", "63417846240", "68702666760", "124884879840", "126713795040", "126835722720" ]
[ "nonn", "base" ]
12
1
1
[ "A000203", "A005100", "A027687", "A068404", "A380845", "A380846", "A380847", "A380848" ]
null
Amiram Eldar, Feb 05 2025
2025-02-12T03:16:38
oeisdata/seq/A380/A380848.seq
d05da8a53700a26110a2c404ef2473c7
A380849
Lesser of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A380845(k) - k is the sum of aliquot divisors of k that have the same binary weight as k.
[ "27940", "112420", "150368", "156840", "225060", "450340", "569376", "925920", "1102200", "1211232", "1802020", "2196592", "2423648", "3377640", "3604260", "4612644", "4874400", "4949160", "5092440", "6375336", "6632808", "6786340", "7155940", "7208740", "7626900", "7685128", "9443060", "9569780", "9643400", "9678020" ]
[ "nonn", "base" ]
9
1
1
[ "A000203", "A002025", "A002046", "A380845", "A380846", "A380849", "A380850" ]
null
Amiram Eldar, Feb 05 2025
2025-02-07T00:44:34
oeisdata/seq/A380/A380849.seq
7e9ae6546750d582c78059979bf24b68
A380850
Greater of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A380845(k) - k is the sum of aliquot divisors of k that have the same binary weight as k.
[ "36068", "145124", "153670", "294075", "290532", "581348", "593100", "1099530", "2066625", "1237830", "2326244", "2338832", "2476870", "6393390", "4652772", "4883976", "6854625", "9279675", "9548325", "6514464", "11725857", "8760548", "9237668", "9305828", "9457356", "8717912", "12190132", "12353716", "10607740", "12493444" ]
[ "nonn", "base" ]
9
1
1
[ "A000203", "A002025", "A002046", "A380845", "A380846", "A380849", "A380850" ]
null
Amiram Eldar, Feb 06 2025
2025-02-07T00:44:41
oeisdata/seq/A380/A380850.seq
e554adf66c23b9e8ee23e98b78c930be
A380851
Riordan array ((1-x)^(m-1), x/(1-x)) with factor r^(2*n) on row n, for m = 3/2, r = 2.
[ "1", "-2", "4", "-2", "8", "16", "-4", "24", "96", "64", "-10", "80", "480", "640", "256", "-28", "280", "2240", "4480", "3584", "1024", "-84", "1008", "10080", "26880", "32256", "18432", "4096", "-264", "3696", "44352", "147840", "236544", "202752", "90112", "16384", "-858", "13728", "192192", "768768", "1537536", "1757184", "1171456", "425984", "65536" ]
[ "sign", "tabl" ]
25
0
2
[ "A002420", "A007318", "A097805", "A104712", "A104713", "A135278", "A159854", "A240530", "A380851" ]
null
Igor Victorovich Statsenko, Feb 06 2025
2025-03-02T02:45:21
oeisdata/seq/A380/A380851.seq
74a9180a364d1fc7f01482cd8bf5aa3c
A380852
a(1) = 2; thereafter a(n) is the least prime which is the sum of two or more consecutive primes starting with a(n-1).
[ "2", "5", "23", "83", "269", "1381", "7039", "21139", "105751", "317279", "7935833", "39679259", "357113983", "73923025091", "517461176119", "29495287085179", "1268297344683899", "21561054859629541", "280293713175186847", "33354951867847517227", "833873796696187941437", "120911700520947252047333", "5199203122400731838067259" ]
[ "nonn" ]
29
1
1
null
null
Andrey Samosyuk, Feb 06 2025
2025-03-26T22:29:18
oeisdata/seq/A380/A380852.seq
b3251fb3c921b220e4d46eb3b2cba65f
A380853
Number of ways to place six distinct positive integers on a triangle, three on the corners and three on the sides such that the sum of the three values on each side is n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "3", "5", "13", "14", "25", "37", "47", "58", "89", "98", "126", "159", "188", "219", "276", "303", "362", "423", "478", "536", "633", "688", "781", "881", "973", "1068", "1211", "1301", "1443", "1589", "1724", "1866", "2066", "2202", "2396", "2598", "2790", "2986", "3250", "3439", "3699", "3967", "4219", "4480", "4819", "5071" ]
[ "nonn", "easy" ]
46
1
10
[ "A342467", "A380105", "A380853" ]
null
Derek Holton and Alex Holton, Feb 06 2025
2025-03-13T06:08:14
oeisdata/seq/A380/A380853.seq
95db1221aa5785037d2f6c7c29acdea5
A380854
Integers m for which m = Sum (d_i + 1)^k, where m is k decimal digits long and d_i are the digits of m.
[ "141", "251", "560", "664807556", "424710875510", "863812804425", "137134427278403350052", "366828486147473227474", "186740753582576522645847734" ]
[ "nonn", "more", "base" ]
8
1
1
[ "A005188", "A261433", "A380810", "A380854" ]
null
Chai Wah Wu, Feb 06 2025
2025-02-07T13:10:53
oeisdata/seq/A380/A380854.seq
0937b2edc69db29179615331b80a0109
A380855
The unique sequence starting with a(0) = 1, a(1) = 0 and partial sums are 1 followed by the sequence terms themselves repeated in successive blocks a(0..2^k-1) for k >= 0.
[ "1", "0", "0", "-1", "1", "-1", "0", "-1", "2", "-1", "0", "-1", "2", "-2", "1", "-1", "2", "-1", "0", "-1", "2", "-2", "1", "-1", "3", "-3", "1", "-1", "3", "-4", "3", "-2", "2", "-1", "0", "-1", "2", "-2", "1", "-1", "3", "-3", "1", "-1", "3", "-4", "3", "-2", "3", "-3", "1", "-1", "3", "-4", "3", "-2", "4", "-6", "4", "-2", "4", "-7", "7", "-5", "3", "-1", "0", "-1", "2", "-2", "1", "-1", "3", "-3", "1", "-1", "3", "-4", "3", "-2", "3", "-3", "1", "-1", "3", "-4", "3" ]
[ "sign", "easy" ]
49
0
9
[ "A053645", "A380855" ]
null
Thomas Scheuerle, Feb 06 2025
2025-02-09T12:20:52
oeisdata/seq/A380/A380855.seq
e3ef18f6396b9baeff28dcf618e91176
A380856
In the binary expansion of n, arrange bits row-wise in a binary tree which is complete except for the last row and then read those bits in pre-order.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "10", "9", "11", "12", "14", "13", "15", "16", "18", "20", "22", "17", "19", "21", "23", "24", "26", "28", "30", "25", "27", "29", "31", "32", "33", "36", "37", "40", "41", "44", "45", "34", "35", "38", "39", "42", "43", "46", "47", "48", "49", "52", "53", "56", "57", "60", "61", "50", "51", "54", "55", "58", "59", "62", "63", "64", "65", "66", "67", "72" ]
[ "nonn", "look", "base" ]
39
0
3
[ "A000079", "A000225", "A007283", "A053738", "A053754", "A335040", "A378496", "A379905", "A380856" ]
null
Darío Clavijo, Feb 06 2025
2025-02-18T07:29:13
oeisdata/seq/A380/A380856.seq
34270d0ea9654cb70015f93e91190557
A380857
Squares of numbers that are neither squarefree nor prime powers.
[ "144", "324", "400", "576", "784", "1296", "1600", "1936", "2025", "2304", "2500", "2704", "2916", "3136", "3600", "3969", "4624", "5184", "5625", "5776", "6400", "7056", "7744", "8100", "8464", "9216", "9604", "9801", "10000", "10816", "11664", "12544", "13456", "13689", "14400", "15376", "15876", "17424", "18225", "18496", "19600", "20736" ]
[ "nonn", "easy" ]
16
1
1
[ "A013661", "A059404", "A082020", "A085548", "A120944", "A126706", "A154945", "A177492", "A286708", "A359280", "A362605", "A378768", "A380857" ]
null
Michael De Vlieger, Feb 06 2025
2025-02-08T23:34:27
oeisdata/seq/A380/A380857.seq
2f8c5d37c9c7382b994f3c44c7fdcde1
A380858
a(n) is the number of primes p <= n such that p^(p + n) == p (mod p + n).
[ "0", "0", "2", "1", "2", "1", "1", "2", "1", "3", "2", "3", "1", "3", "2", "3", "2", "4", "1", "3", "1", "3", "1", "6", "0", "6", "1", "4", "2", "7", "1", "3", "0", "6", "3", "6", "1", "5", "2", "5", "2", "8", "1", "5", "1", "5", "1", "8", "0", "6", "2", "5", "1", "9", "0", "8", "1", "5", "3", "12", "1", "8", "1", "7", "2", "11", "1", "8", "2", "8", "2", "10", "1", "6", "0", "9", "1", "12", "1", "7", "1", "5", "1", "13", "0", "9", "3", "6", "1", "15" ]
[ "nonn", "look" ]
18
1
3
[ "A000040", "A371883", "A380858" ]
null
Juri-Stepan Gerasimov, Feb 06 2025
2025-03-13T08:56:37
oeisdata/seq/A380/A380858.seq
8fd80e9b95d4150f36854e4e41a36fa5
A380859
Number of minimum connected dominating sets in the n-triangular honeycomb obtuse knight graph.
[ "1", "0", "0", "0", "0", "630", "36", "4", "12" ]
[ "nonn", "more" ]
39
1
6
null
null
Eric W. Weisstein, Mar 05 2025
2025-03-22T10:24:00
oeisdata/seq/A380/A380859.seq
70eeb6adaeadddd0ae74408ed2e0f425
A380860
Triangle read by rows: T(n,m) (0<=m<=n) = number of positive n-digit numbers that have exactly m copies of a specific, previously selected positive base-10 digit among its digits.
[ "1", "8", "1", "72", "17", "1", "648", "225", "26", "1", "5832", "2673", "459", "35", "1", "52488", "29889", "6804", "774", "44", "1", "472392", "321489", "91125", "13770", "1170", "53", "1", "4251528", "3365793", "1141614", "215055", "24300", "1647", "62", "1", "38263752", "34543665", "13640319", "3077109", "433755", "39123", "2205", "71", "1", "344373768", "349156737", "157306536", "41334300", "6980904", "785862", "58968", "2844", "80", "1" ]
[ "nonn", "base", "tabl" ]
25
0
2
[ "A052268", "A055275", "A081044", "A380860" ]
null
Peter Starek, Feb 06 2025
2025-02-07T16:34:14
oeisdata/seq/A380/A380860.seq
96c7f64f6f6cc8a9d5cce234a93637d1
A380861
Decimal expansion of the smallest acute vertex angle, in radians, in a deltoidal hexecontahedron face.
[ "1", "1", "8", "3", "0", "3", "6", "7", "2", "8", "4", "2", "0", "0", "8", "3", "4", "1", "4", "7", "9", "0", "1", "3", "6", "1", "8", "6", "7", "9", "9", "8", "8", "7", "8", "6", "5", "0", "5", "4", "8", "2", "0", "6", "6", "8", "3", "6", "8", "4", "0", "6", "3", "5", "9", "7", "6", "6", "7", "9", "2", "8", "5", "3", "3", "5", "5", "6", "4", "0", "7", "3", "1", "4", "3", "9", "9", "2", "7", "5", "3", "9", "6", "4", "9", "4", "8", "8", "0", "3" ]
[ "nonn", "cons", "easy" ]
13
1
3
[ "A002163", "A379385", "A379386", "A379387", "A379388", "A379389", "A380861", "A380862", "A380863" ]
null
Paolo Xausa, Feb 06 2025
2025-02-08T03:43:57
oeisdata/seq/A380/A380861.seq
45593ac57a4766d72e012c663c5ec259
A380862
Decimal expansion of the largest acute angles, in radians, in a deltoidal hexecontahedron face.
[ "1", "5", "1", "7", "9", "8", "5", "3", "7", "7", "4", "6", "0", "2", "1", "5", "4", "6", "3", "6", "0", "2", "1", "9", "1", "3", "5", "7", "3", "8", "6", "0", "7", "2", "4", "4", "8", "1", "7", "1", "2", "3", "3", "3", "8", "2", "5", "2", "7", "1", "6", "7", "2", "3", "0", "1", "0", "8", "0", "7", "6", "0", "2", "2", "4", "5", "5", "8", "8", "5", "1", "8", "3", "5", "3", "0", "5", "5", "1", "6", "4", "4", "8", "8", "2", "5", "1", "1", "8", "9" ]
[ "nonn", "cons", "easy" ]
11
1
2
[ "A020762", "A379385", "A379386", "A379387", "A379388", "A379389", "A380861", "A380862", "A380863" ]
null
Paolo Xausa, Feb 06 2025
2025-02-08T03:43:47
oeisdata/seq/A380/A380862.seq
4654b792b00a033c007af12daa0a5bed
A380863
Decimal expansion of the obtuse vertex angle, in radians, in a deltoidal hexecontahedron face.
[ "2", "0", "6", "4", "1", "7", "7", "8", "2", "3", "8", "3", "9", "0", "7", "2", "1", "3", "4", "9", "3", "0", "7", "6", "7", "8", "6", "4", "9", "8", "6", "9", "7", "3", "0", "0", "6", "9", "9", "7", "0", "5", "1", "3", "6", "5", "3", "2", "7", "4", "7", "0", "8", "2", "1", "9", "6", "6", "9", "4", "4", "2", "8", "6", "3", "4", "8", "2", "2", "1", "7", "1", "4", "0", "7", "1", "3", "8", "7", "1", "6", "7", "8", "4", "1", "5", "5", "7", "8", "3" ]
[ "nonn", "cons", "easy" ]
8
1
1
[ "A002163", "A379385", "A379386", "A379387", "A379388", "A379389", "A380861", "A380862", "A380863" ]
null
Paolo Xausa, Feb 07 2025
2025-02-08T03:43:41
oeisdata/seq/A380/A380863.seq
3993aede067fffd417f105480cb2c43d
A380864
a(n) = [x^n] sqrt(1 - 4*x)/(1 - 8*x). Row sums of A380865.
[ "1", "6", "46", "364", "2902", "23188", "185420", "1483096", "11863910", "94908420", "759257636", "6074027496", "48592102396", "388736403144", "3109889739352", "24879112565936", "199032881137798", "1592262978387044", "12738103567806772", "101904827587176776", "815238617162887828", "6521908924174861784" ]
[ "nonn" ]
11
0
2
[ "A380864", "A380865" ]
null
Peter Luschny, Feb 06 2025
2025-02-08T04:53:51
oeisdata/seq/A380/A380864.seq
5e82d3d5e6cd420d26edaea81bf91b1a
A380865
Triangle read by rows: T(n, k) = 2^(2*n)*JacobiP(n - k, k, -1/2 - n, -1).
[ "1", "2", "4", "6", "24", "16", "20", "120", "160", "64", "70", "560", "1120", "896", "256", "252", "2520", "6720", "8064", "4608", "1024", "924", "11088", "36960", "59136", "50688", "22528", "4096", "3432", "48048", "192192", "384384", "439296", "292864", "106496", "16384", "12870", "205920", "960960", "2306304", "3294720", "2928640", "1597440", "491520", "65536" ]
[ "nonn", "tabl" ]
11
0
2
[ "A038234", "A097807", "A128908", "A380851", "A380864", "A380865" ]
null
Peter Luschny, Feb 07 2025
2025-02-08T04:48:20
oeisdata/seq/A380/A380865.seq
d5f25d64607f3136b3d394222233a2d6
A380866
a(n) is the least m > 0 such that sigma(m) - 2m = A140863(n).
[ "18", "196", "100", "36", "15376", "162", "1352", "72", "968", "200", "392", "13456", "144", "8450", "1032256", "400", "119072", "324", "8464", "288", "1936", "5776", "2704", "4624", "111392", "450", "800", "1458", "9604", "2450", "1568", "882", "2500", "576", "648", "89888", "3872", "5408", "1600", "70688", "2178", "9248", "11552", "11025", "59168", "53792", "3136", "16928", "1152", "900", "43808", "26912", "3042", "30752" ]
[ "nonn" ]
8
1
1
[ "A000203", "A033880", "A140863", "A380866" ]
null
M. F. Hasler, Mar 10 2025
2025-03-12T08:18:45
oeisdata/seq/A380/A380866.seq
46170d145e98eeccbd3861368b35f86c
A380867
Numbers k such that one can make a rectangle from a chain of linked rods of length 1, 2, 3, ..., k, with perimeter equal to the total length.
[ "8", "15", "20", "24", "27", "32", "35", "39", "44", "48", "51", "55", "56", "63", "68", "75", "80", "84", "87", "92", "95", "99", "104", "111", "115", "116", "119", "120", "123", "124", "128", "132", "135", "140", "143", "144", "147", "152", "155", "159", "160", "164", "168", "171", "175", "176", "183", "184", "188", "195", "200", "203", "204", "207", "208", "212", "215", "216", "219", "220", "224", "231", "235", "236" ]
[ "nonn", "nice" ]
11
1
1
[ "A000217", "A334720", "A380867" ]
null
Ali Sada and M. F. Hasler, Mar 14 2025
2025-03-14T21:08:34
oeisdata/seq/A380/A380867.seq
2e1115465bd57adc5e7cd73e7f3384be
A380868
Number of distinct solutions {n1, n2, n3, n4} to the problem of forming a rectangle with sides made of linked rods of length 1, ..., n.
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "3", "0", "0", "0", "1", "0", "0", "3", "0", "0", "0", "0", "1", "0", "0", "6", "0", "0", "0", "6", "0", "0", "0", "0", "6", "0", "0", "0", "1", "0", "0", "3", "0", "0", "0", "3", "3", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "3", "0", "0", "0", "0", "0", "0", "6", "0", "0", "0", "0", "6", "0", "0", "0", "10", "0", "0", "3", "0", "0", "0", "0", "3", "0", "0", "1", "0", "0", "0", "15" ]
[ "nonn" ]
24
1
20
[ "A000217", "A334720", "A380867", "A380868" ]
null
M. F. Hasler, Mar 14 2025
2025-03-22T18:40:39
oeisdata/seq/A380/A380868.seq
df64871688b1311f33c5e8f5043dd4b4
A380869
Numbers k such that one can make a rectangle from a chain of linked rods of lengths 1, 2, 3, ..., k, with perimeter equal to the total length, and with one side consisting of a single rod.
[ "8", "15", "20", "24", "27", "35", "39", "80", "84", "104", "143", "215", "220", "252", "264", "351", "363", "459", "476" ]
[ "nonn", "more" ]
12
1
1
[ "A000217", "A334720", "A380867", "A380868", "A380869" ]
null
Ali Sada and M. F. Hasler, Mar 14 2025
2025-03-18T10:52:19
oeisdata/seq/A380/A380869.seq
8719eebdd9c548877046909c64eb12e2
A380870
a(n) = A381798(n) - A361373(n) - 1.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "3", "0", "0", "2", "0", "1", "4", "6", "0", "0", "0", "8", "0", "1", "0", "1", "0", "0", "3", "3", "7", "2", "0", "13", "0", "1", "0", "4", "0", "7", "6", "6", "0", "1", "0", "15", "14", "8", "0", "13", "3", "0", "15", "23", "0", "1", "0", "0", "5", "0", "5", "7", "0", "3", "9", "12", "0", "2", "0", "30", "18", "14", "10", "6", "0", "3", "0", "14", "0" ]
[ "nonn" ]
12
1
15
[ "A000961", "A024619", "A361373", "A377485", "A380870", "A381750", "A381798", "A381799" ]
null
Michael De Vlieger, Apr 08 2025
2025-04-12T12:42:53
oeisdata/seq/A380/A380870.seq
0d793d7dad780449e6f08f2a8bbf6ec3
A380871
Limit of the trajectory of n under A380873: concatenate sum and product of digits, if it ends on a fixed point, otherwise the least element of the limit cycle.
[ "0", "50", "70", "70", "70", "80", "1236", "40", "88", "10", "10", "50", "50", "60", "20", "50", "70", "50", "70", "10", "20", "50", "70", "50", "70", "80", "70", "10", "80", "90", "30", "60", "50", "70", "60", "90", "90", "40", "88", "90", "40", "20", "70", "60", "70", "20", "70", "40", "70", "10", "50", "50", "80", "90", "20", "80", "50", "50", "80", "40", "60", "70", "70", "90", "70", "50", "1236", "70", "70", "70", "70", "50", "10" ]
[ "nonn" ]
9
0
2
[ "A007953", "A007954", "A062237", "A380871", "A380872", "A380873" ]
null
M. F. Hasler, Apr 02 2025
2025-04-04T22:36:35
oeisdata/seq/A380/A380871.seq
e7db19bfb50c0174e79c57ef44b9c4f0
A380872
Infinite square array, where row r >= 0 is the orbit of r under the map A380873: concatenate(sum of digits, product of digits).
[ "0", "0", "1", "0", "11", "2", "0", "21", "22", "3", "0", "32", "44", "33", "4", "0", "56", "816", "69", "44", "5", "0", "1130", "1548", "1554", "816", "55", "6", "0", "50", "18160", "15100", "1548", "1025", "66", "7", "0", "50", "160", "70", "18160", "80", "1236", "77", "8", "0", "50", "70", "70", "160", "80", "1236", "1449", "88", "9", "0", "50", "70", "70", "70", "80", "1236", "18144", "1664", "99", "10", "0", "50", "70", "70", "70", "80", "1236", "18128", "17144", "1881", "10", "11", "0", "50", "70", "70", "70", "80", "1236", "20128", "17112", "1864" ]
[ "nonn", "base", "tabl" ]
15
0
5
[ "A007953", "A007954", "A271220", "A271268", "A380872", "A380873" ]
null
M. F. Hasler, Apr 01 2025
2025-04-04T22:37:13
oeisdata/seq/A380/A380872.seq
a5208f08920a8fbe0d7d96ade131a676
A380873
Concatenate sum and product of decimal digits of n.
[ "0", "11", "22", "33", "44", "55", "66", "77", "88", "99", "10", "21", "32", "43", "54", "65", "76", "87", "98", "109", "20", "32", "44", "56", "68", "710", "812", "914", "1016", "1118", "30", "43", "56", "69", "712", "815", "918", "1021", "1124", "1227", "40", "54", "68", "712", "816", "920", "1024", "1128", "1232", "1336", "50", "65", "710", "815", "920", "1025", "1130", "1235", "1340", "1445", "60" ]
[ "nonn", "base" ]
16
0
2
[ "A007953", "A007954", "A062237", "A271220", "A271268", "A380872", "A380873" ]
null
M. F. Hasler, Apr 01 2025
2025-04-12T18:19:25
oeisdata/seq/A380/A380873.seq
035e73fa79b7aabf09358af29bf01cbe
A380874
Indices of odd values > 1 in A067044 (least k such that k*n has only even digits).
[ "16", "54", "58", "74", "76", "92", "94", "96", "98", "118", "126", "128", "136", "148", "154", "156", "158", "160", "162", "164", "168", "176", "182", "184", "186", "188", "196", "216", "218", "238", "252", "254", "272", "274", "276", "292", "294", "296", "298", "316", "318", "326", "346", "352", "364", "366", "372", "376", "382", "384", "386", "388", "392" ]
[ "nonn", "base" ]
4
1
1
[ "A067044", "A380874" ]
null
M. F. Hasler, Mar 07 2025
2025-03-07T09:24:12
oeisdata/seq/A380/A380874.seq
008862a91d4e2c368cb6f34026661c59
A380875
Indices of triangular numbers (A000217) which are also perimeters of integer-sided right triangles (A010814).
[ "8", "15", "20", "23", "24", "27", "32", "35", "39", "44", "47", "48", "51", "55", "56", "59", "60", "63", "64", "68", "71", "72", "75", "76", "79", "80", "84", "87", "91", "92", "95", "96", "99", "104", "111", "112", "115", "116", "119", "120", "123", "124", "128", "132", "135", "139", "140", "143", "144", "147", "152", "155", "159", "160", "164", "167", "168", "171", "175", "176", "179", "180", "183", "184", "187", "188" ]
[ "nonn" ]
13
1
1
[ "A000217", "A010814", "A380875", "A382268" ]
null
M. F. Hasler, Mar 20 2025
2025-04-02T10:21:59
oeisdata/seq/A380/A380875.seq
ffe2a390abe5e32d27aa7c7b7e7593e0
A380876
a(1) = 1; a(2) = 4; for n > 2, a(n) = least unused positive y such that gcd(y,n-1) > 1 and |y-n| > 1.
[ "1", "4", "6", "9", "2", "10", "3", "14", "12", "15", "5", "22", "8", "26", "7", "18", "20", "34", "16", "38", "24", "27", "11", "46", "21", "30", "13", "33", "32", "58", "25", "62", "28", "36", "17", "40", "39", "74", "19", "42", "35", "82", "45", "86", "48", "50", "23", "94", "44", "56", "54", "57", "60", "106", "51", "65", "49", "63", "29", "118", "52", "122", "31", "66", "68", "55", "64", "134", "72" ]
[ "nonn" ]
19
1
2
null
null
Ali Sada, Feb 06 2025
2025-02-18T18:38:18
oeisdata/seq/A380/A380876.seq
7dbb52b2e61007663b735860b1493435
A380877
Primes p where the prime race 12m+1 versus 12m+7 is tied.
[ "2", "3", "5", "13", "17", "433", "457", "461" ]
[ "nonn" ]
10
1
1
[ "A007351", "A068228", "A068229", "A379989", "A380333", "A380877" ]
null
Ya-Ping Lu, Feb 06 2025
2025-03-03T10:47:28
oeisdata/seq/A380/A380877.seq
e1d0c945553a0025e682c1cbc6417d16
A380878
Numbers k such that k*(k+1) shares no decimal digits with k or k+1.
[ "2", "3", "4", "5", "6", "7", "8", "15", "17", "18", "22", "24", "32", "33", "34", "37", "42", "43", "44", "45", "47", "48", "53", "54", "55", "56", "57", "58", "65", "66", "76", "77", "78", "83", "85", "92", "143", "144", "148", "154", "156", "165", "175", "188", "194", "195", "222", "232", "237", "242", "257", "265", "292", "294", "303", "307", "312", "313", "322", "332", "333", "334", "343", "344", "375", "377", "387", "392" ]
[ "nonn", "base" ]
14
1
1
[ "A375211", "A380878" ]
null
Robert Israel, Feb 07 2025
2025-02-07T16:00:50
oeisdata/seq/A380/A380878.seq
f1d12fa7f9577a386b435b58877d3ed1
A380879
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x*exp(x)) ).
[ "1", "2", "16", "230", "4888", "138442", "4916140", "210270734", "10530743632", "604747157138", "39185881490644", "2828691317839510", "225137088955561144", "19588316964130880474", "1849745928662841982588", "188421660506420000503838", "20594905554562935801454240", "2404374864844251715105658146" ]
[ "nonn" ]
10
0
2
[ "A162695", "A360474", "A380879", "A380880" ]
null
Seiichi Manyama, Feb 07 2025
2025-02-07T05:36:43
oeisdata/seq/A380/A380879.seq
f2394a180937875c17e5697c774b2a7b
A380880
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x*exp(x)) ).
[ "1", "3", "33", "657", "19317", "756663", "37153071", "2196991317", "152107121481", "12074764795947", "1081507189545219", "107911010079715857", "11871250914793342797", "1427601609871824349407", "186326851375925627135127", "26232637698244127999077677", "3962908338833364902518738449", "639433805204122165558890771027" ]
[ "nonn" ]
11
0
2
[ "A162695", "A380879", "A380880", "A380881" ]
null
Seiichi Manyama, Feb 07 2025
2025-02-07T05:36:34
oeisdata/seq/A380/A380880.seq
4b03b19ec98db58b1e97fdbe86fd5e0a
A380881
E.g.f. A(x) satisfies A(x) = exp( x * A(x)^3 * exp(x * A(x)^3) ).
[ "1", "1", "9", "163", "4541", "171781", "8231395", "478055299", "32642065433", "2562896897353", "227510655792191", "22533214047347455", "2463465770439307045", "294676777871863052173", "38284087227668033391515", "5368383942726216941810971", "808133883137288259018215345", "129988823008132636178027546257" ]
[ "nonn" ]
11
0
3
[ "A162695", "A360474", "A362656", "A380880", "A380881" ]
null
Seiichi Manyama, Feb 07 2025
2025-02-07T05:36:28
oeisdata/seq/A380/A380881.seq
194d41e8d74788700ae0cb658b818765
A380882
Centered square numbers which are sphenic numbers.
[ "1105", "2665", "3445", "7565", "8845", "14965", "15665", "16745", "17485", "18241", "20605", "22685", "23545", "27145", "28085", "32005", "32513", "35113", "37265", "48985", "50245", "50881", "55445", "56785", "62305", "71065", "74885", "78013", "80401", "81205", "84461", "85285", "88621", "89465", "109045", "111865", "113765", "116645", "118585", "119561" ]
[ "nonn" ]
13
1
1
[ "A001844", "A007304", "A027862", "A370795", "A371016", "A380882" ]
null
Massimo Kofler, Feb 07 2025
2025-03-02T23:54:35
oeisdata/seq/A380/A380882.seq
2f936f4c1fa7643c72a993eee5d58c2d
A380883
a(n) is the smallest multiple of prime(n) which contains every decimal digit of prime(n), including repetitions.
[ "12", "30", "15", "70", "110", "130", "170", "190", "230", "290", "310", "370", "164", "344", "470", "530", "295", "610", "670", "710", "730", "790", "830", "890", "679", "1010", "1030", "1070", "1090", "1130", "1270", "1310", "1370", "1390", "1490", "1510", "1570", "1630", "1670", "1730", "1790", "1810", "1719", "1930", "1379", "1990", "2110", "2230", "2270", "2290", "2330", "2390", "2410", "1255", "2570", "2367", "2690" ]
[ "nonn", "base" ]
13
1
1
[ "A000040", "A087217", "A380811", "A380883" ]
null
David James Sycamore, Feb 07 2025
2025-02-23T11:24:42
oeisdata/seq/A380/A380883.seq
7b134967715fa939a3a7177e3ea751a7
A380884
Primes p such that there is an m < 10 for which m*p contains every decimal digit of p.
[ "2", "5", "41", "43", "59", "97", "191", "197", "251", "263", "373", "401", "443", "491", "499", "599", "653", "691", "967", "991", "997", "1481", "1901", "1913", "1997", "2549", "2551", "2591", "3067", "3491", "4001", "4013", "4493", "4793", "4931", "4943", "4967", "4973", "4993", "4999", "5021", "5443", "5647", "6053", "6361", "6521", "6703", "6991", "7489", "7901", "7951", "7993" ]
[ "nonn", "base" ]
13
1
1
[ "A000040", "A380811", "A380883", "A380884" ]
null
David James Sycamore, Feb 07 2025
2025-02-23T11:18:23
oeisdata/seq/A380/A380884.seq
6cf78ad4c6390aab43e8c3bcd4a3ed47
A380885
a(n) is the smallest multiple m*n (m > 1) of n which contains every decimal digit of n, including repetitions.
[ "10", "12", "30", "24", "15", "36", "70", "48", "90", "100", "110", "120", "130", "140", "105", "160", "170", "108", "190", "120", "126", "220", "230", "240", "125", "260", "270", "280", "290", "300", "310", "320", "330", "340", "315", "360", "370", "380", "390", "240", "164", "294", "344", "440", "405", "460", "470", "384", "294", "150", "153", "520", "530", "540" ]
[ "nonn", "base" ]
24
1
1
[ "A087217", "A380885" ]
null
David James Sycamore, Feb 07 2025
2025-02-23T11:19:08
oeisdata/seq/A380/A380885.seq
ad4e49ed4b6d1f9d735abac120547270
A380886
Triangle T(n,k), 1<=k<=n: column k are the coefficients of the INVERT transform of Sum_{i=1..k} i*x^i.
[ "1", "1", "3", "1", "5", "8", "1", "11", "17", "21", "1", "21", "42", "50", "55", "1", "43", "100", "128", "138", "144", "1", "85", "235", "323", "358", "370", "377", "1", "171", "561", "813", "923", "965", "979", "987", "1", "341", "1331", "2043", "2378", "2510", "2559", "2575", "2584", "1", "683", "3158", "5150", "6125", "6527", "6681", "6737", "6755", "6765", "1", "1365", "7503", "12967", "15772", "16972", "17441", "17617", "17680", "17700", "17711" ]
[ "nonn", "tabl", "easy" ]
10
1
3
[ "A001045", "A001906", "A054452", "A101822", "A322059", "A380886" ]
null
R. J. Mathar, Feb 07 2025
2025-02-07T09:11:52
oeisdata/seq/A380/A380886.seq
d09bad25055209b87b05265239342f1d
A380887
a(n) is the smallest positive integer s that can be partitioned into n positive integers whose product is s * 100^(n-1).
[ "1", "400", "525", "644", "759", "864", "972", "1089", "1188", "1296", "1403", "1508", "1612", "1722", "1827", "1932", "2040", "2145", "2250", "2354", "2457", "2565", "2668", "2772", "2880", "2988", "3087", "3192", "3294", "3399", "3498", "3604" ]
[ "nonn", "more", "changed" ]
64
1
2
[ "A380887", "A381187", "A381619", "A381621", "A382547" ]
null
Markus Sigg, Feb 07 2025
2025-04-23T10:46:50
oeisdata/seq/A380/A380887.seq
f6a36a4a8b29d08ec3a15139632a0746
A380888
Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = -1.
[ "2", "9", "75", "625", "1029", "1365", "8575", "11375", "24843", "32955", "73815", "117649", "156065", "207025", "274625", "483153", "599781", "615125", "866481", "1008273", "1252815", "1337505", "1343433", "1553937", "1782105", "1955085", "2061345", "2840383", "3051015", "3432165", "3737085", "3767855", "4026275", "4998175" ]
[ "nonn", "changed" ]
20
1
1
[ "A036878", "A380888", "A380889", "A380900", "A380901", "A380923", "A380928" ]
null
Paolo P. Lava, Feb 07 2025
2025-04-25T18:18:26
oeisdata/seq/A380/A380888.seq
aab09beb6bb4d85b0002dbe36b3413f0
A380889
Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = 1.
[ "8", "81", "90", "100", "132", "1125", "1250", "1323", "1470", "1485", "1650", "2156", "2178", "2420", "2898", "3220", "6348", "6612", "12948", "15625", "18375", "20625", "21609", "24010", "24255", "26950", "27225", "30250", "35574", "35937", "36225", "39930", "40250", "47334", "47817", "53130", "58564", "71415", "74385", "77924", "79350" ]
[ "nonn", "easy" ]
9
1
1
[ "A380888", "A380889", "A380900", "A380901", "A380923", "A380928" ]
null
Paolo P. Lava, Feb 07 2025
2025-03-02T23:48:02
oeisdata/seq/A380/A380889.seq
a6f1c0a08c8af26e8ce35d30c04054ef
A380890
Triangle T(n,k) read by rows: the number of graphs with n nodes which are enriched cycles (necklaces) and the elements in the cycle are marked linear chains up to length k.
[ "1", "1", "2", "1", "2", "4", "1", "3", "5", "7", "1", "3", "7", "9", "12", "1", "5", "14", "18", "21", "24", "1", "5", "19", "29", "35", "38", "42", "1", "8", "35", "56", "71", "77", "81", "85", "1", "10", "60", "100", "133", "148", "156", "160", "165", "1", "15", "107", "192", "264", "297", "317", "325", "330", "335", "1", "19", "187", "361", "511", "586", "630", "650", "660", "665", "671", "1", "31", "352", "714", "1041", "1206", "1306", "1350", "1375", "1385", "1391", "1397" ]
[ "nonn", "tabl" ]
10
1
3
[ "A000358", "A322059", "A380890" ]
null
R. J. Mathar, Feb 07 2025
2025-02-10T04:57:58
oeisdata/seq/A380/A380890.seq
a2c15475f4699e77dd35ecd3785d89c8
A380891
If n mod 2 = 0 then a(n) = floor(n^(1/3)) else a(n) = floor(n^(4/3)).
[ "0", "1", "1", "4", "1", "8", "1", "13", "2", "18", "2", "24", "2", "30", "2", "36", "2", "43", "2", "50", "2", "57", "2", "65", "2", "73", "2", "81", "3", "89", "3", "97", "3", "105", "3", "114", "3", "123", "3", "132", "3", "141", "3", "150", "3", "160", "3", "169", "3", "179", "3", "189", "3", "199", "3", "209", "3", "219", "3", "229", "3", "240", "3", "250", "4", "261", "4", "272" ]
[ "nonn", "easy" ]
30
0
4
[ "A048766", "A094683", "A129011", "A380891" ]
null
Vikram Prasad, Feb 08 2025
2025-04-12T09:50:34
oeisdata/seq/A380/A380891.seq
5bd173acfcb76e3d913387e154b51801
A380892
Hexagonal numbers that are abundant.
[ "66", "120", "276", "378", "630", "780", "1128", "1326", "1540", "1770", "2016", "2556", "2850", "3160", "3486", "3828", "4560", "4950", "5778", "6216", "7140", "7626", "7875", "8646", "9180", "9730", "10296", "10878", "12090", "12720", "14028", "14706", "15400", "16110", "16836", "17955", "18336", "19110", "19900", "20706", "21528", "21945", "23220", "24090", "24976" ]
[ "nonn" ]
19
1
1
[ "A000384", "A005101", "A063734", "A074315", "A117794", "A379264", "A380892" ]
null
Massimo Kofler, Feb 07 2025
2025-02-24T21:22:40
oeisdata/seq/A380/A380892.seq
9e8e333ba7d40d7fdf64956b591fde5b
A380893
Triangle read by rows: T(n,m) = number of solid partitions of n with shape of a plane partition of m.
[ "1", "1", "3", "1", "3", "6", "1", "6", "6", "13", "1", "6", "15", "13", "24", "1", "9", "21", "37", "24", "48", "1", "9", "30", "58", "75", "48", "86", "1", "12", "39", "95", "132", "159", "86", "160", "1", "12", "54", "128", "231", "297", "299", "160", "282", "1", "15", "63", "197", "345", "552", "593", "574", "282", "500", "1", "15", "81", "251", "546", "873", "1156", "1180", "1038", "500", "859", "1", "18", "96", "345", "771", "1452", "1933", "2390", "2208", "1874", "859", "1479", "1", "18", "114", "432", "1110", "2151", "3340", "4154", "4614", "4082", "3268", "1479", "2485", "1", "21", "132", "558", "1491", "3276", "5214", "7430", "8310", "8758", "7276", "5685", "2485", "4167" ]
[ "nonn", "tabl" ]
11
1
3
[ "A000219", "A000293", "A094504", "A380893" ]
null
Wouter Meeussen, Feb 07 2025
2025-02-10T01:05:29
oeisdata/seq/A380/A380893.seq
8bbbbcf99af5c25450581704f81ed38a
A380894
a(1) = 0; a(2) = 1; for n > 2, a(n) = a(n-1) + least unique positive difference of two earlier terms.
[ "0", "1", "2", "4", "7", "11", "16", "22", "32", "44", "58", "76", "96", "121", "147", "177", "208", "241", "277", "314", "352", "392", "435", "480", "527", "579", "636", "694", "754", "815", "878", "943", "1014", "1086", "1159", "1235", "1312", "1390", "1470", "1551", "1634", "1719", "1806", "1894", "1989", "2085", "2185", "2286", "2389", "2494", "2600", "2709" ]
[ "nonn" ]
12
1
3
[ "A000045", "A002858", "A380894" ]
null
Felix Huber, Feb 10 2025
2025-03-04T23:01:38
oeisdata/seq/A380/A380894.seq
3768d127c6eac6e4ab863ec45d837a6c
A380895
Decimal expansion of (sqrt(17) + 1)/(4*sqrt(17)).
[ "3", "1", "0", "6", "3", "3", "9", "0", "6", "2", "5", "9", "0", "8", "3", "2", "4", "3", "3", "7", "9", "7", "2", "6", "6", "1", "5", "5", "2", "9", "0", "3", "0", "5", "4", "4", "4", "8", "7", "4", "5", "8", "8", "1", "2", "1", "3", "7", "8", "4", "7", "3", "5", "9", "3", "2", "9", "3", "9", "1", "6", "7", "0", "1", "9", "2", "5", "7", "2", "8", "5", "8", "0", "3", "4", "3", "7", "6", "7", "8", "8", "1", "4", "0", "9", "9", "7", "9", "9", "4", "8", "6", "4", "8", "6", "3", "0", "0", "4", "3" ]
[ "nonn", "cons", "easy" ]
13
0
1
[ "A010473", "A222132", "A380895", "A380896" ]
null
Stefano Spezia, Feb 07 2025
2025-02-08T12:59:46
oeisdata/seq/A380/A380895.seq
a07b88a61bd9698f996e17a8e9c81199
A380896
Decimal expansion of (sqrt(17) - 1)/(4*sqrt(17)).
[ "1", "8", "9", "3", "6", "6", "0", "9", "3", "7", "4", "0", "9", "1", "6", "7", "5", "6", "6", "2", "0", "2", "7", "3", "3", "8", "4", "4", "7", "0", "9", "6", "9", "4", "5", "5", "5", "1", "2", "5", "4", "1", "1", "8", "7", "8", "6", "2", "1", "5", "2", "6", "4", "0", "6", "7", "0", "6", "0", "8", "3", "2", "9", "8", "0", "7", "4", "2", "7", "1", "4", "1", "9", "6", "5", "6", "2", "3", "2", "1", "1", "8", "5", "9", "0", "0", "2", "0", "0", "5", "1", "3", "5", "1", "3", "6", "9", "9", "5", "6" ]
[ "nonn", "cons", "easy" ]
12
0
2
[ "A010473", "A222132", "A380895", "A380896" ]
null
Stefano Spezia, Feb 07 2025
2025-02-08T13:00:55
oeisdata/seq/A380/A380896.seq
992a23c90552b70879e779146d86b254
A380897
Decimal expansion of (108)^(1/5).
[ "2", "5", "5", "0", "8", "4", "9", "0", "0", "1", "2", "5", "1", "5", "8", "1", "6", "6", "5", "7", "3", "3", "0", "9", "5", "7", "0", "0", "3", "8", "5", "9", "9", "8", "5", "4", "6", "5", "8", "9", "8", "0", "0", "1", "6", "7", "3", "8", "3", "9", "6", "4", "5", "4", "7", "3", "7", "8", "0", "1", "9", "6", "3", "6", "2", "1", "1", "4", "3", "4", "4", "6", "8", "6", "0", "6", "9", "4", "7", "1", "3", "1", "1", "0", "3", "5", "1", "4", "8", "7", "3", "0", "7", "9", "5", "8", "6", "4", "4", "0" ]
[ "nonn", "cons", "easy" ]
8
1
1
[ "A222132", "A380897" ]
null
Stefano Spezia, Feb 07 2025
2025-02-08T03:43:33
oeisdata/seq/A380/A380897.seq
9e78fe86bb83c8be9b25ccbd9578e6e9
A380898
Decimal expansion of 2^(8/3).
[ "6", "3", "4", "9", "6", "0", "4", "2", "0", "7", "8", "7", "2", "7", "9", "7", "8", "9", "9", "0", "0", "6", "8", "2", "2", "5", "5", "7", "0", "8", "9", "2", "3", "3", "0", "4", "1", "5", "6", "5", "9", "7", "3", "3", "1", "1", "5", "9", "9", "4", "1", "2", "0", "3", "9", "2", "3", "3", "1", "4", "3", "0", "4", "7", "3", "0", "0", "8", "6", "6", "0", "2", "2", "4", "9", "6", "8", "7", "6", "6", "9", "3", "0", "9", "4", "1", "7", "6", "8", "5", "3", "0", "4", "8", "8", "8", "3", "8", "2", "8" ]
[ "nonn", "cons", "easy" ]
11
1
1
[ "A002580", "A010588", "A010603", "A380898" ]
null
Stefano Spezia, Feb 07 2025
2025-02-08T09:02:32
oeisdata/seq/A380/A380898.seq
730588bd30a825d08f1ecf3843054522
A380899
Three-Catalan Triangle read by rows, for n>=0 and k>=0.
[ "1", "1", "1", "1", "1", "4", "9", "11", "10", "6", "3", "1", "34", "90", "120", "120", "96", "64", "35", "15", "5", "1", "364", "1000", "1400", "1505", "1351", "1044", "700", "406", "202", "84", "28", "7", "1", "4269", "11925", "17225", "19425", "18657", "15753", "11845", "7965", "4785", "2553", "1197", "485", "165", "45", "9", "1" ]
[ "nonn", "tabf" ]
12
0
6
[ "A005721", "A008287", "A380899" ]
null
Michel Marcus, Feb 07 2025
2025-02-10T03:13:12
oeisdata/seq/A380/A380899.seq
9ce4091333894c24ade6267a16c8ecea
A380900
Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = -2.
[ "3", "125", "16807", "29155", "33275", "50575", "90475", "7761061", "8857805", "11796113", "13463065", "20462645", "21102389", "24084445", "35496425", "36606185", "63500525", "65485805", "73776725", "99798725", "113597825", "117779585", "178056445", "193155305", "200599525", "203878325", "204311525", "251218345" ]
[ "nonn" ]
9
1
1
[ "A380888", "A380889", "A380900", "A380901", "A380923", "A380928" ]
null
Paolo P. Lava, Feb 09 2025
2025-03-02T23:48:09
oeisdata/seq/A380/A380900.seq
09821e196997573611b1de5d787cdaaa
A380901
Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = 2.
[ "16", "243", "78125", "120393", "166725", "177957", "316953", "792585", "1478925", "40353607", "55883275", "59648043", "77389375", "82602975", "88167807", "106237047", "107171875", "114391875", "122098275", "128153375", "130323843", "147121275", "157032603", "177471875", "189427875", "190142667", "203739375", "217464975" ]
[ "nonn" ]
8
1
1
[ "A380888", "A380889", "A380900", "A380901", "A380923", "A380928" ]
null
Paolo P. Lava, Mar 03 2025
2025-03-16T08:08:05
oeisdata/seq/A380/A380901.seq
cfc87bcf7d4b5e4985283131e942e8ac
A380902
Integers k with at least 1 proper factorization for which the sum of the squares of the factors equals k.
[ "16", "27", "48", "54", "270", "528", "1755", "7216", "7830", "11934", "69168", "81702", "100368", "264654", "340470", "559899", "1397808", "1586340", "1695195", "3837510", "3918420", "8989110", "9815568", "13010448", "15812550", "19468816", "26302590", "75872430", "132825616", "133529580", "180280539", "271165488" ]
[ "nonn" ]
24
1
1
[ "A001694", "A005117", "A162247", "A190882", "A380760", "A380902" ]
null
Charles L. Hohn, Feb 07 2025
2025-03-25T08:59:35
oeisdata/seq/A380/A380902.seq
444f965ce1b83a467f77bee1edecfb67
A380903
Least positive k such that n^n * k^k - 1 is a prime, or 0 if no such k exists.
[ "2", "2", "1", "2", "3", "4", "10147", "24" ]
[ "nonn", "hard", "more" ]
8
0
1
[ "A228175", "A231119", "A231735", "A380903" ]
null
Jason Yuen, Feb 07 2025
2025-02-10T09:33:11
oeisdata/seq/A380/A380903.seq
58b0d4300c855a408e045cebff6ef21c
A380904
An integer sequence giving a counterexample to a theorem of Szüsz and Volkmann.
[ "0", "10", "20", "30", "40", "50", "60", "70", "80", "90", "100", "110", "120", "130", "140", "150", "160", "170", "180", "190", "200", "210", "220", "230", "240", "250", "260", "270", "280", "290", "300", "310", "320", "330", "340", "350", "360", "370", "380", "390", "400", "410", "420", "430", "440", "450", "460", "470", "480", "490", "500", "510", "520", "530", "540", "550", "560", "570", "580", "590", "600", "610", "620", "630", "640", "650", "660", "670", "680", "690", "700", "710", "720", "730", "740", "750", "760", "770", "780", "790", "800", "810", "820", "830", "840", "850", "860", "870", "880", "890", "900", "1000", "1100", "1200", "1300", "1400", "1500", "1600", "1700", "1800", "1900", "2000", "2100", "2200", "2300", "2400", "2500", "2600", "2700", "2800", "2900", "3000" ]
[ "nonn" ]
44
9
2
[ "A008592", "A380904" ]
null
John M. Campbell, Feb 07 2025
2025-03-03T14:52:26
oeisdata/seq/A380/A380904.seq
d8afe39b66087f0f52b8f67c7aba3e90
A380905
Smallest number k such that k^(2*3^n) - 6 is prime.
[ "3", "5", "23", "7", "433", "2447", "9377", "82597", "134687" ]
[ "nonn", "more", "hard", "changed" ]
151
0
1
[ "A008776", "A025192", "A028879", "A239414", "A380905", "A382246" ]
null
Jakub Buczak, Feb 07 2025
2025-04-17T09:34:12
oeisdata/seq/A380/A380905.seq
e4861096dd956855134f097b75b27140
A380906
Primes avoiding the digits 3 and 5.
[ "2", "7", "11", "17", "19", "29", "41", "47", "61", "67", "71", "79", "89", "97", "101", "107", "109", "127", "149", "167", "179", "181", "191", "197", "199", "211", "227", "229", "241", "269", "271", "277", "281", "401", "409", "419", "421", "449", "461", "467", "479", "487", "491", "499", "601", "607", "617", "619", "641", "647", "661", "677", "691", "701", "709", "719", "727", "761", "769", "787", "797" ]
[ "base", "nonn" ]
27
1
1
[ "A000040", "A020462", "A038611", "A038613", "A329760", "A380906" ]
null
Vincenzo Librandi, Feb 09 2025
2025-02-12T21:53:10
oeisdata/seq/A380/A380906.seq
bdef3d8e3be619f0306ca3ec509bc4af