A296133 Number of twice-factorizations of n of type (Q,R,Q).

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 2, 2, 3, 1, 5, 1, 3, 2, 2, 2, 7, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 7, 1, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 9, 1, 2, 3, 6, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 7, 2, 2, 1, 9, 2, 2, 2

Offset: 1

Author

Gus Wiseman, Dec 05 2017

Keywords

• nonn

Examples

			The a(36) = 7 twice-factorizations are (2*3)*(6), (6)*(2*3), (2*3*6), (2*18), (3*12), (4*9), (36).
		

Crossrefs

Cf. A000005, A001055, A005117, A045778, A052409, A052410, A089723, A279790, A279791, A284639, A292886, A296132.

Programs

Mathematica

sfs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[sfs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Length[Join@@Function[fac,Select[Join@@Permutations/@sps[fac],SameQ@@Times@@@#&]]/@sfs[n]],{n,100}]