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

1,6

Links

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

Example

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

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}]

Crossrefs

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

Sequence in context: A323091 A045778 A320889 * A338649 A337176 A033103

Adjacent sequences: A296130 A296131 A296132 * A296134 A296135 A296136

Keyword

nonn

Author

Gus Wiseman, Dec 05 2017

Status

approved