cp's OEIS Frontend

A325509 Number of factorizations of n! into factorial numbers > 1.

%I A325509 #17 May 12 2019 17:11:43
%S A325509 1,1,1,1,2,1,2,1,2,2,3,1,2,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,2,1,
%T A325509 1,1,2,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,
%U A325509 1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1
%N A325509 Number of factorizations of n! into factorial numbers > 1.
%F A325509 a(n) = 1 + A034876(n).
%e A325509 n = 10:
%e A325509   (6*120*5040)
%e A325509   (720*5040)
%e A325509   (3628800)
%e A325509 n = 16:
%e A325509   (2*2*2*2*1307674368000)
%e A325509   (2*120*87178291200)
%e A325509   (20922789888000)
%e A325509 n = 24:
%e A325509   (2*2*6*25852016738884976640000)
%e A325509   (24*25852016738884976640000)
%e A325509   (620448401733239439360000)
%t A325509 facs[n_,u_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d,u],Min@@#>=d&]],{d,Intersection[u,Rest[Divisors[n]]]}]];
%t A325509 Table[Length[facs[n!,Rest[Array[#!&,n]]]],{n,15}]
%Y A325509 Cf. A000142, A011371, A022559, A034876, A034878, A076934, A109100, A109101, A109102, A115627, A135291, A322583, A325272, A325273, A325276, A325508, A325510, A325511.
%K A325509 nonn
%O A325509 0,5
%A A325509 _Gus Wiseman_, May 08 2019
%E A325509 More terms from _Alois P. Heinz_, May 08 2019