cp's OEIS Frontend

A294786 Number of ways to choose a set partition of a factorization of n into distinct factors greater than one such that different blocks have different products.

%I A294786 #10 Nov 24 2017 11:47:12
%S A294786 1,1,1,1,1,3,1,3,1,3,1,5,1,3,3,3,1,5,1,5,3,3,1,12,1,3,3,5,1,12,1,5,3,
%T A294786 3,3,11,1,3,3,12,1,12,1,5,5,3,1,19,1,5,3,5,1,12,3,12,3,3,1,26,1,3,5,9,
%U A294786 3,12,1,5,3,12,1,26,1,3,5,5,3,12,1,19,3,3
%N A294786 Number of ways to choose a set partition of a factorization of n into distinct factors greater than one such that different blocks have different products.
%H A294786 Michael De Vlieger, <a href="/A294786/b294786.txt">Table of n, a(n) for n = 1..16384</a>
%F A294786 a(product of n distinct primes) = A000258(n).
%F A294786 a(prime^n) = A279375(n).
%e A294786 The a(36)=11 ways are:
%e A294786 (2)*(3)*(6),
%e A294786 (2)*(3*6), (2*6)*(3), (2)*(18), (3)*(12), (4)*(9),
%e A294786 (2*3*6), (2*18), (3*12), (4*9), (36).
%t A294786 sfs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[sfs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A294786 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A294786 Table[Length[Join@@Function[fac,Select[sps[fac],UnsameQ@@Times@@@#&]]/@sfs[n]],{n,100}]
%Y A294786 Cf. A000258, A001055, A045778, A279375, A281113, A294787, A294788.
%K A294786 nonn
%O A294786 1,6
%A A294786 _Gus Wiseman_, Nov 08 2017