A085288 Number of sorted multiplicative partitions of n!.

1, 1, 3, 3, 10, 10, 30, 75, 220, 220, 588, 588, 1568, 3696, 11616, 11616, 30492, 30492, 84700, 173250, 441000, 441000, 1262520, 2777544, 6957720, 16731660, 43506760, 43506760, 98658000, 98658000, 277101000, 541886400, 1322481600, 2715495552

Offset: 2

Author

Eric W. Weisstein, Jun 23 2003

Keywords

• nonn

Comments

Number of decompositions of n! into factors of the form (p_k)^(e^k).

Examples

			4! = 3*8 = 2*3*4 = 2*2*2*3, so a(4)=3.
5! = 3*5*8 = 2*3*4*5 = 2*2*2*3*5, so a(5)=3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..6940
• Eric Weisstein's World of Mathematics, Alladi-Grinstead Constant

Crossrefs

Cf. A000142, A000688, A085289, A085290, A085291.

Programs

Mathematica

f[n_] := Times @@ PartitionsP /@ Last /@ FactorInteger[ n!]; Array[f, 34, 2] (* Robert G. Wilson v, Sep 22 2006 *)

Formula

a(n) = A000688(n!) = A000688(A000142(n)). - Vladeta Jovovic, Jun 27 2003

Extensions

More terms from Vladeta Jovovic, Jun 27 2003