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A322886 Number of 3-generated Abelian groups of order A025487(n).

%I A322886 #8 Jan 02 2019 11:53:37
%S A322886 1,1,2,1,3,2,4,3,1,5,4,4,2,7,6,5,3,8,8,4,7,1,9,4,10,10,6,8,2,12,5,12,
%T A322886 14,8,10,3,15,8,7,14,9,16,4,16,10,12,4,21,12,8,16,12,20,1,6,20,14,14,
%U A322886 5,24,16,10,19,15,24,2,8,28,18,16,16,8,16,7,30,20,9,12,25,21,21,28,3
%N A322886 Number of 3-generated Abelian groups of order A025487(n).
%C A322886 Groups generated by fewer than 3 elements are not excluded. The number of Abelian groups with 3 invariant factors is a(n) - A052304(n).
%C A322886 Sum of the first three columns from A249771 (for n > 1).
%H A322886 Jean-François Alcover, <a href="/A322886/b322886.txt">Table of n, a(n) for n = 1..300</a>
%F A322886 a(n) = A322885(A025487(n)).
%t A322886 terms = 300; nmax = 15 terms^2;
%t A322886 A025487 = Module[{lpe = {}, ln = {1}}, Do[pe = FactorInteger[n][[All, 2]] // Sort; If[FreeQ[lpe, pe], AppendTo[lpe, pe]; AppendTo[ln, n]], {n, 2, nmax}]; ln];
%t A322886 a322885[n_] := Times @@ (Round[(#+3)^2/12]& /@ FactorInteger[n][[All, 2]]);
%t A322886 a[n_] := a322885[A025487[[n]]];
%t A322886 Array[a, terms] (* _Jean-François Alcover_, Jan 02 2019, after _Robert G. Wilson v_ in A025487 *)
%Y A322886 Cf. A052304, A025487, A249771, A322885.
%K A322886 nonn
%O A322886 1,3
%A A322886 _Álvar Ibeas_, Dec 29 2018