A075071 n! divided by product of factorials of all proper divisors of n, as n runs through the values for which the result is an integer.

1, 2, 6, 12, 120, 60, 5040, 840, 60480, 15120, 39916800, 2310, 6227020800, 8648640, 1816214400, 10810800, 355687428096000, 2042040, 121645100408832000, 116396280, 1689515283456000, 14079294028800, 25852016738884976640000

Offset: 1

Author

Amarnath Murthy, Sep 09 2002

Keywords

• nice
• nonn

Comments

n! divided by the product of factorials of all proper divisors of n is not always an integer; e.g., when n = 24 the quotient is 7436429/48. See A075422.

Examples

			a(12) = 12! / (2!*3!*4!*6!) = 2310.
		

Crossrefs

Cf. A075422.

Programs

Mathematica

Select[Table[ n!/ Apply[ Times, Drop[ Divisors[n], -1]! ], {n, 1, 23}], IntegerQ]
Select[Table[n!/Times@@(Most[Divisors[n]]!),{n,30}],IntegerQ] (* Harvey P. Dale, Aug 01 2020 *)

Extensions

Edited by Robert G. Wilson v, Sep 14 2002

First Mathematica program modified by Harvey P. Dale, Aug 01 2020