A306268 Number of ways to choose a strict factorization into squarefree factors of each factor in a strict factorization of n.

1, 1, 1, 0, 1, 3, 1, 0, 0, 3, 1, 3, 1, 3, 3, 0, 1, 3, 1, 3, 3, 3, 1, 1, 0, 3, 0, 3, 1, 12, 1, 0, 3, 3, 3, 5, 1, 3, 3, 1, 1, 12, 1, 3, 3, 3, 1, 0, 0, 3, 3, 3, 1, 1, 3, 1, 3, 3, 1, 19, 1, 3, 3, 0, 3, 12, 1, 3, 3, 12, 1, 4, 1, 3, 3, 3, 3, 12, 1, 0, 0, 3, 1, 19, 3

Offset: 1

Author

Gus Wiseman, Feb 01 2019

Keywords

• nonn

Examples

			The a(216) = 8 factorizations:
   (2*3)*(2*3*6)    (2*6)*(3*6)
  (2)*(2*3)*(3*6)   (6)*(2*3*6)
  (2)*(3)*(2*3*6)  (2)*(6)*(3*6)
  (3)*(2*3)*(2*6)  (3)*(6)*(2*6)
		

Crossrefs

Cf. A001055, A000258, A050326, A050336, A296118, A296120.

Programs

Mathematica

facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
Table[Length[Join@@Table[Tuples[Select[facs[#],And[UnsameQ@@#,And@@SquareFreeQ/@#]&]&/@fac],{fac,Select[facs[n],UnsameQ@@#&]}]],{n,60}]