A323090 Number of strict factorizations of n using elements of A007916 (numbers that are not perfect powers).

1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 2, 1, 2, 2, 0, 1, 2, 1, 2, 2, 2, 1, 2, 0, 2, 0, 2, 1, 5, 1, 0, 2, 2, 2, 3, 1, 2, 2, 2, 1, 5, 1, 2, 2, 2, 1, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 7, 1, 2, 2, 0, 2, 5, 1, 2, 2, 5, 1, 4, 1, 2, 2, 2, 2, 5, 1, 2, 0, 2, 1, 7, 2, 2, 2

Offset: 1

Author

Gus Wiseman, Jan 04 2019

Keywords

• nonn

Examples

			The a(72) = 4 factorizations are (2*3*12), (3*24), (6*12), (72). Missing from this list and not strict are (2*2*2*3*3), (2*2*3*6), (2*6*6), (2*2*18), while missing from the list and using perfect powers are (2*36), (2*4*9), (3*4*6), (4*18), (8*9).
		

Crossrefs

Positions of 0's are A246547.

Positions of 1's are A000040.

Positions of 2's are A084227.

Positions of 3's are A085986.

Positions of 4's are A143610.

Cf. A001055, A001597, A007916, A025147, A045778, A052410, A303707, A323054, A323087, A323088, A323089.

Programs

Mathematica

radQ[n_]:=Or[n==1,GCD@@FactorInteger[n][[All,2]]==1];
facssr[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facssr[n/d],Min@@#>d&]],{d,Select[Rest[Divisors[n]],radQ]}]];
Table[Length[facssr[n]],{n,100}]