OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Boris Horvat, Gašper Jaklič, and Tomaž Pisanski, On the number of hamiltonian groups, Mathematical Communications, Vol. 10, No. 1 (2005), pp. 89-94; arXiv preprint, arXiv:math/0503183 [math.CO], 2005.
Hong-Quan Liu, On the number of abelian groups of a given order (supplement), Acta Arithmetica, Vol. 64, No. 3 (1993), pp. 285-296.
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
More accurately, a(n) = A021002 * n + A084892 * n^(1/2) + A084893 * n^(1/3) + O(n^(50/199 + eps)), where eps>0 is arbitrarily small (Liu, 1993). - Amiram Eldar, Sep 23 2023
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
KEYWORD
nonn
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Sep 04 2001
EXTENSIONS
More terms from James A. Sellers, Sep 26 2001
STATUS
approved