A301856 - OEIS

%I #5 Apr 08 2018 20:09:25

%S 0,1,1,3,1,4,1,7,3,4,1,12,1,4,4,14,1,12,1,12,4,4,1,29,3,4,7,12,1,17,1,

%T 27,4,4,4,36,1,4,4,29,1,17,1,12,12,4,1,62,3,12,4,12,1,29,4,29,4,4,1,

%U 53,1,4,12,47,4,17,1,12,4,17,1,90,1,4,12,12,4,17

%N Number of subset-products (greater than 1) of factorizations of n into factors greater than 1.

%C 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.

%e The a(12) = 12 subset-products:

%e 12<=(2*2*3), 6<=(2*2*3), 4<=(2*2*3), 3<=(2*2*3), 2<=(2*2*3),

%e 12<=(2*6),   6<=(2*6),   4<=(3*4),   3<=(3*4),   2<=(2*6),

%e 12<=(3*4),

%e 12<=(12).

%e The a(16) = 14 subset-products:

%e 16<=(16),

%e 16<=(4*4),

%e 16<=(2*8),     8<=(2*8),     4<=(4*4),     2<=(2*8),

%e 16<=(2*2*4),   8<=(2*2*4),   4<=(2*2*4),   2<=(2*2*4),

%e 16<=(2*2*2*2), 8<=(2*2*2*2), 4<=(2*2*2*2), 2<=(2*2*2*2).

%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];

%t Table[Sum[Length[Union[Times@@@Rest[Subsets[f]]]],{f,facs[n]}],{n,100}]

%Y Cf. A001055, A000712, A045778, A108917, A162247, A276024, A281116, A284640, A292886, A301829, A301830.

%K nonn

%O 1,4

%A _Gus Wiseman_, Mar 27 2018