%I #4 Oct 22 2018 12:42:56
%S 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,
%T 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,
%U 2,4,1,7,1,2,3,3,2,4,1,5,3,2,1,7,2,2,2
%N Number of factorizations of n into primes or semiprimes.
%e 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).
%t psemfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[psemfacs[n/d],Min@@#>=d&]],{d,Select[Rest[Divisors[n]],PrimeOmega[#]<=2&]}]];
%t Table[Length[psemfacs[n]],{n,100}]
%Y Cf. A001055, A001222, A001358, A007716, A007717, A037143, A045778, A320663, A320655.
%K nonn
%O 1,4
%A _Gus Wiseman_, Oct 20 2018