cp's OEIS Frontend

A296120 Number of ways to choose a strict factorization of each factor in a strict factorization of n.

%I A296120 #6 Dec 19 2017 02:39:50
%S A296120 1,1,1,1,1,3,1,3,1,3,1,6,1,3,3,4,1,6,1,6,3,3,1,13,1,3,3,6,1,12,1,7,3,
%T A296120 3,3,14,1,3,3,13,1,12,1,6,6,3,1,25,1,6,3,6,1,13,3,13,3,3,1,31,1,3,6,
%U A296120 11,3,12,1,6,3,12,1,36,1,3,6,6,3,12,1,25,4,3
%N A296120 Number of ways to choose a strict factorization of each factor in a strict factorization of n.
%F A296120 Dirichlet g.f.: Product_{n > 1}(1 + A045778(n)/n^s).
%e A296120 The a(36) = 14 twice-factorizations:
%e A296120 (36), (4*9), (3*12), (2*18), (2*3*6),
%e A296120 (4)*(9), (3)*(12), (3)*(3*4), (3)*(2*6), (2)*(18), (2)*(3*6), (2)*(2*9),
%e A296120 (2)*(3)*(6), (2)*(3)*(2*3).
%t A296120 sfs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[sfs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A296120 Table[Sum[Times@@Length/@sfs/@fac,{fac,sfs[n]}],{n,100}]
%Y A296120 Cf. A000009, A005117, A045778, A050345, A279785, A281113, A294788, A296118, A296119, A296121.
%K A296120 nonn
%O A296120 1,6
%A A296120 _Gus Wiseman_, Dec 05 2017