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A085288 Number of sorted multiplicative partitions of n!. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

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

LINKS

Table of n, a(n) for n=2..35.

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. 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

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Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)