A323087 Number of strict factorizations of n into factors > 1 such that no factor is a power of any other factor.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 5, 1, 2, 2, 2, 2, 5, 1, 2, 2, 4, 1, 5, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 9, 1, 2, 3, 1, 2, 5, 1, 3, 2, 5, 1, 8, 1, 2, 3, 3, 2, 5, 1, 5, 1, 2, 1, 9, 2, 2, 2

Offset: 1

Author

Gus Wiseman, Jan 04 2019

Keywords

• nonn

Examples

			The a(60) = 9 factorizations:
  (2*3*10), (2*5*6), (3*4*5),
  (2*30), (3*20), (4*15), (5*12), (6*10),
  (60).
		

Crossrefs

Cf. A001597, A007916, A025147, A045778, A052410, A087897, A275972, A305150, A323054, A323086, A323090, A323091.

Programs

Mathematica

strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
Table[Length[Select[strfacs[n],stableQ[#,IntegerQ[Log[#1,#2]]&]&]],{n,100}]