OFFSET
1,4
COMMENTS
For a finite multiset p of positive integers greater than 1 with product n, a pair (t > 1, p) is defined to be a subset-product if there exists a nonempty submultiset of p with product t.
EXAMPLE
The a(12) = 12 subset-products:
12<=(2*2*3), 6<=(2*2*3), 4<=(2*2*3), 3<=(2*2*3), 2<=(2*2*3),
12<=(2*6), 6<=(2*6), 4<=(3*4), 3<=(3*4), 2<=(2*6),
12<=(3*4),
12<=(12).
The a(16) = 14 subset-products:
16<=(16),
16<=(4*4),
16<=(2*8), 8<=(2*8), 4<=(4*4), 2<=(2*8),
16<=(2*2*4), 8<=(2*2*4), 4<=(2*2*4), 2<=(2*2*4),
16<=(2*2*2*2), 8<=(2*2*2*2), 4<=(2*2*2*2), 2<=(2*2*2*2).
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Sum[Length[Union[Times@@@Rest[Subsets[f]]]], {f, facs[n]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 27 2018
STATUS
approved