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

2,3

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 2..6940

Eric Weisstein's World of Mathematics, Alladi-Grinstead Constant

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A168376 A266221 A073709 * A124630 A321397 A128015

Adjacent sequences: A085285 A085286 A085287 * A085289 A085290 A085291

Keyword

nonn

Author

Eric W. Weisstein, Jun 23 2003

Extensions

More terms from Vladeta Jovovic, Jun 27 2003

Status

approved