

A322886


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


1



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
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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

JeanFrançois 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] (* JeanFrançois 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



