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A075072
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a(1) = 1; for n > 1, a(n) = n! divided by product of factorials of all prime divisors of n.
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0
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1, 1, 1, 12, 1, 60, 1, 20160, 60480, 15120, 1, 39916800, 1, 8648640, 1816214400, 10461394944000, 1, 533531142144000, 1, 10137091700736000, 1689515283456000, 14079294028800, 1, 51704033477769953280000, 129260083694424883200000, 32382376266240000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Terms are always integers by the following classical theorem: let x(i) be k positive integers such that x(1)+x(2)+...+x(k) <= n, then x(1)!*x(2)!*...*x(k)! divides n! - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 16 2002
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EXAMPLE
| a(12) = 12! / { 2!*3!) = 39916800.
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MATHEMATICA
| Table[n!/Times@@(First[Transpose[FactorInteger[n]]]!), {n, 30}] (* From Harvey P. Dale, May 07 2011 *)
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CROSSREFS
| Sequence in context: A013619 A092527 A085840 * A038327 A157780 A010204
Adjacent sequences: A075069 A075070 A075071 * A075073 A075074 A075075
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KEYWORD
| nice,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 09 2002
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EXTENSIONS
| a(26) from Harvey P. Dale, May 07 2011.
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