OFFSET
1,6
COMMENTS
a(n) is the number of ways to choose a product-preserving permutation of a set partition of a factorization of n into distinct factors greater than one.
EXAMPLE
The a(36) = 13 twice-factorizations are: (2)*(3)*(6), (2)*(3*6), (6)*(2*3), (2*3)*(6), (2*6)*(3), (2*3*6), (2)*(18), (2*18), (3)*(12), (3*12), (4)*(9), (4*9), (36).
MATHEMATICA
nn=100;
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[Total[Sum[Times@@Factorial/@Length/@Split[Sort[Times@@@f]], {f, sps[Sort[#]]}]&/@sfs[n]], {n, nn}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 08 2017
STATUS
approved