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

1,3

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

Formula

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

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 *)

Crossrefs

Cf. A052304, A025487, A249771, A322885.

Sequence in context: A051282 A274121 A052306 * A320642 A046823 A224989

Adjacent sequences: A322883 A322884 A322885 * A322887 A322888 A322889

Keyword

nonn

Author

Álvar Ibeas, Dec 29 2018

Status

approved