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A322885 Number of 3-generated Abelian groups of order n. 1
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

Table of n, a(n) for n=1..102.

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

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 A227350

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 March 26 00:29 EDT 2019. Contains 321479 sequences. (Running on oeis4.)