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

1,6

Links

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

Example

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).

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}]

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.

Sequence in context: A177207 A161528 A175083 * A355935 A180026 A136176

Adjacent sequences: A323087 A323088 A323089 * A323091 A323092 A323093

Keyword

nonn

Author

Gus Wiseman, Jan 04 2019

Status

approved