cp's OEIS Frontend

A299764 Number of special products of factorizations of n into factors > 1.

%I A299764 #16 Jun 10 2018 21:15:55
%S A299764 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 A299764 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 A299764 64,2,6,16,51,6,22,2,16,6,22,2,104,2,6,16,16,6
%N A299764 Number of special products of factorizations of n into factors > 1.
%C A299764 A special product of a factorization f is a number n > 0 such that exactly one submultiset of f has product n.
%e A299764 The a(12) = 16 special subset-products:
%e A299764 1<=(12), 12<=(12),
%e A299764 1<=(2*6), 2<=(2*6), 6<=(2*6), 12<=(2*6),
%e A299764 1<=(3*4), 3<=(3*4), 4<=(3*4), 12<=(3*4),
%e A299764 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 A299764 The a(16) = 18 special subset-products:
%e A299764 1<=(16), 16<=(16),
%e A299764 1<=(4*4), 4<=(4*4), 16<=(4*4),
%e A299764 1<=(2*8), 2<=(2*8), 8<=(2*8), 16<=(2*8),
%e A299764 1<=(2*2*4), 2<=(2*2*4), 8<=(2*2*4), 16<=(2*2*4),
%e A299764 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 A299764 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A299764 sppr[y_]:=Join@@Select[GatherBy[Union[Subsets[y]],Times@@#&],Length[#]===1&];
%t A299764 Table[Length[Join@@sppr/@facs[n]],{n,30}]
%Y A299764 Cf. A001055, A292886, A299701, A301829, A301830, A301854, A301957, A301979, A304796.
%K A299764 nonn
%O A299764 1,2
%A A299764 _Gus Wiseman_, Jun 08 2018