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

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, 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, 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

Offset: 1

Author

Álvar Ibeas, Dec 29 2018

Keywords

• nonn

Comments

Groups generated by fewer than 3 elements are not excluded. The number of Abelian groups with 3 invariant factors is a(n) - A052304(n).

Sum of the first three columns from A249771 (for n > 1).

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A052304, A025487, A249771, A322885.

Programs

Mathematica

terms = 300; nmax = 15 terms^2;
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];
a322885[n_] := Times @@ (Round[(#+3)^2/12]& /@ FactorInteger[n][[All, 2]]);
a[n_] := a322885[A025487[[n]]];
Array[a, terms] (* Jean-François Alcover, Jan 02 2019, after Robert G. Wilson v in A025487 *)

Formula

a(n) = A322885(A025487(n)).