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

Author

Gus Wiseman, Sep 15 2019

Keywords

• nonn

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

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

Programs

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}]

Formula

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