A325509 - OEIS

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A325509

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..105.

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}]

CROSSREFS

Cf. A000142, A011371, A022559, A034876, A034878, A076934, A109100, A109101, A109102, A115627, A135291, A322583, A325272, A325273, A325276, A325508, A325510, A325511.

Sequence in context: A025817 A109381 A058506 * A324117 A106698 A097848

Adjacent sequences: A325506 A325507 A325508 * A325510 A325511 A325512

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 08 2019

EXTENSIONS

More terms from Alois P. Heinz, May 08 2019

STATUS

approved