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 A322885 Number of 3-generated Abelian groups of order n. 2
 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 7, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 5, 1, 2, 2, 4, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Groups generated by fewer than 3 elements are not excluded. The number of Abelian groups with 3 invariant factors is a(n) - A046951(n). Sum of the first three columns from A249770 (for n > 1). Dirichlet convolution of A061704 and A010052. Dirichlet convolution of A046951 and A010057. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(p^e) = A001399(e). Dirichlet g.f.: zeta(s) * zeta(2s) * zeta(3s). Sum_{k=1..n} a(k) ~ Pi^2*Zeta(3)*n/6 + Zeta(1/2)*Zeta(3/2)*sqrt(n) + Zeta(1/3)*Zeta(2/3)*n^(1/3). - Vaclav Kotesovec, Feb 02 2019 MAPLE f:= proc(n) local t;   mul(round((t[2]+3)^2/12), t=ifactors(n)[2]) end proc: map(f, [\$1..200]); # Robert Israel, May 20 2019 MATHEMATICA a[n_] := Times @@ (Round[(# + 3)^2/12]& /@ FactorInteger[n][[All, 2]]); Array[a, 102] (* Jean-François Alcover, Jan 02 2019 *) CROSSREFS Cf. A001399, A010052, A010057, A046951, A061704, A249770. Sequence in context: A091050 A005361 A303915 * A292582 A008479 A331178 Adjacent sequences:  A322882 A322883 A322884 * A322886 A322887 A322888 KEYWORD nonn,mult AUTHOR Álvar Ibeas, Dec 29 2018 STATUS approved

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Last modified April 7 19:24 EDT 2020. Contains 333306 sequences. (Running on oeis4.)