OFFSET
1,6
COMMENTS
A strict planar branching factorization of n is either the number n itself or a sequence of at least two strict planar branching factorizations, one of each factor in a strict ordered factorization of n. A strict planar branching factorization is complete if the leaves are all prime numbers.
EXAMPLE
The a(12) = 4 trees: (2*(2*3)), (2*(3*2)), ((2*3)*2), ((3*2)*2).
MATHEMATICA
ordfacs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@ordfacs[n/d], {d, Rest[Divisors[n]]}]]
sotfs[n_]:=Prepend[Join@@Table[Tuples[sotfs/@f], {f, Select[ordfacs[n], And[Length[#]>1, UnsameQ@@#]&]}], n];
Table[Length[Select[sotfs[n], FreeQ[#, _Integer?(!PrimeQ[#]&)]&]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 11 2018
STATUS
approved