login
A325509
Number of factorizations of n! into factorial numbers > 1.
9
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, 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, 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
OFFSET
0,5
FORMULA
a(n) = 1 + A034876(n).
EXAMPLE
n = 10:
(6*120*5040)
(720*5040)
(3628800)
n = 16:
(2*2*2*2*1307674368000)
(2*120*87178291200)
(20922789888000)
n = 24:
(2*2*6*25852016738884976640000)
(24*25852016738884976640000)
(620448401733239439360000)
MATHEMATICA
facs[n_, u_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d, u], Min@@#>=d&]], {d, Intersection[u, Rest[Divisors[n]]]}]];
Table[Length[facs[n!, Rest[Array[#!&, n]]]], {n, 15}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 08 2019
EXTENSIONS
More terms from Alois P. Heinz, May 08 2019
STATUS
approved