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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 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.)