

A063966


Number of Abelian groups of order <= n.


8



1, 2, 3, 5, 6, 7, 8, 11, 13, 14, 15, 17, 18, 19, 20, 25, 26, 28, 29, 31, 32, 33, 34, 37, 39, 40, 43, 45, 46, 47, 48, 55, 56, 57, 58, 62, 63, 64, 65, 68, 69, 70, 71, 73, 75, 76, 77, 82, 84, 86, 87, 89, 90, 93, 94, 97, 98, 99, 100, 102, 103, 104, 106, 117, 118, 119, 120, 122
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OFFSET

1,2


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
B. Horvat, G. Jaklic and T. Pisanski, On the number of Hamiltonian groups, arXiv:math/0503183 [math.CO], 2005.
Eric Weisstein's World of Mathematics, Abelian Group


FORMULA

a(n) ~ c * n, where c = A021002 = Product_{k>=2} Zeta(k).  Vaclav Kotesovec, Oct 26 2019


MAPLE

with(combinat): readlib(ifactors): total := 0: for n from 1 to 100 do ans := 1: for i from 1 to nops(ifactors(n)[2]) do ans := ans*numbpart(ifactors(n)[2][i][2]) od: printf(`%d, `, total+ans): total := total+ans: od:


MATHEMATICA

Accumulate[Table[FiniteAbelianGroupCount[n], {n, 1, 200}]] (* Geoffrey Critzer, Dec 28 2014 *)


CROSSREFS

Partial sums of A000688.
Cf. A063756.
Sequence in context: A094180 A116545 A140661 * A123030 A284836 A267300
Adjacent sequences: A063963 A063964 A063965 * A063967 A063968 A063969


KEYWORD

nonn


AUTHOR

Ahmed Fares (ahmedfares(AT)mydeja.com), Sep 04 2001


EXTENSIONS

More terms from James A. Sellers, Sep 26 2001


STATUS

approved



