A320732 Number of factorizations of n into primes or semiprimes.

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, 6, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 5, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 7, 1, 2, 3, 4, 2, 4, 1, 3, 2, 4, 1, 7, 1, 2, 3, 3, 2, 4, 1, 5, 3, 2, 1, 7, 2, 2, 2

Offset: 1

Author

Gus Wiseman, Oct 20 2018

Keywords

• nonn

Examples

			The a(60) = 5 factorizations are (2*2*3*5), (2*2*15), (2*3*10), (2*5*6), (3*4*5), (4*15), (6*10).
		

Crossrefs

Cf. A001055, A001222, A001358, A007716, A007717, A037143, A045778, A320663, A320655.

Programs

Mathematica

psemfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[psemfacs[n/d],Min@@#>=d&]],{d,Select[Rest[Divisors[n]],PrimeOmega[#]<=2&]}]];
Table[Length[psemfacs[n]],{n,100}]