A075072 a(1) = 1; for n > 1, a(n) = n! divided by product of factorials of all prime divisors of n.

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

Offset

1,4

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, Sep 16 2002

Links

T. D. Noe, Table of n, a(n) for n = 1..400

Example

a(12) = 12! / (2!*3!) = 39916800.

Mathematica

Table[n!/Times@@(First[Transpose[FactorInteger[n]]]!), {n, 30}] (* Harvey P. Dale, May 07 2011 *)

Crossrefs

Cf. A056218 (multiplicity of prime divisors taken into account).

Sequence in context: A277799 A278468 A280975 * A265825 A347492 A038327

Adjacent sequences: A075069 A075070 A075071 * A075073 A075074 A075075

Keyword

nice,nonn,easy

Author

Amarnath Murthy, Sep 09 2002

Extensions

a(26) from Harvey P. Dale, May 07 2011

Status

approved