A299764 - OEIS

%I #16 Jun 10 2018 21:15:55

%S 1,2,2,5,2,6,2,10,5,6,2,16,2,6,6,18,2,16,2,16,6,6,2,36,5,6,10,16,2,22,

%T 2,32,6,6,6,44,2,6,6,36,2,22,2,16,16,6,2,72,5,16,6,16,2,36,6,36,6,6,2,

%U 64,2,6,16,51,6,22,2,16,6,22,2,104,2,6,16,16,6

%N Number of special products of factorizations of n into factors > 1.

%C A special product of a factorization f is a number n > 0 such that exactly one submultiset of f has product n.

%e The a(12) = 16 special subset-products:

%e 1<=(12), 12<=(12),

%e 1<=(2*6), 2<=(2*6), 6<=(2*6), 12<=(2*6),

%e 1<=(3*4), 3<=(3*4), 4<=(3*4), 12<=(3*4),

%e 1<=(2*2*3), 2<=(2*2*3), 3<=(2*2*3), 4<=(2*2*3), 6<=(2*2*3), 12<=(2*2*3).

%e The a(16) = 18 special subset-products:

%e 1<=(16), 16<=(16),

%e 1<=(4*4), 4<=(4*4), 16<=(4*4),

%e 1<=(2*8), 2<=(2*8), 8<=(2*8), 16<=(2*8),

%e 1<=(2*2*4), 2<=(2*2*4), 8<=(2*2*4), 16<=(2*2*4),

%e 1<=(2*2*2*2), 2<=(2*2*2*2), 4<=(2*2*2*2), 8<=(2*2*2*2), 16<=(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 sppr[y_]:=Join@@Select[GatherBy[Union[Subsets[y]],Times@@#&],Length[#]===1&];

%t Table[Length[Join@@sppr/@facs[n]],{n,30}]

%Y Cf. A001055, A292886, A299701, A301829, A301830, A301854, A301957, A301979, A304796.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jun 08 2018