A327521 Number of factorizations of the n-th squarefree number A005117(n) into squarefree numbers > 1.

1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 5, 1, 2, 2, 2, 1, 2, 2, 1, 5, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 5, 1, 2, 5, 1, 1, 2, 2, 5, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 5, 1, 5, 2, 1, 1, 5, 2, 1, 5, 2, 2, 2, 2, 2, 1, 2, 5, 1, 2, 2, 1, 5, 1, 2

Offset

1,5

Links

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

a(n) = A050320(A005117(n)) = A000110(A072047(n)) = A000110(A001222(A005117(n))).

Mathematica

nn=100;
facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];
y=Select[Range[nn], SquareFreeQ];
Table[Length[facsusing[Rest[y], n]], {n, y}]

Crossrefs

See link for additional cross-references.

Cf. A000110, A005117, A007947, A034444, A050320, A072047, A259936.

Sequence in context: A329618 A026517 A072047 * A282870 A106802 A269254

Adjacent sequences: A327518 A327519 A327520 * A327522 A327523 A327524

Keyword

nonn

Author

Gus Wiseman, Sep 15 2019

Status

approved