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

1,2

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.

Links

Table of n, a(n) for n=1..23.

Example

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

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 *)

Crossrefs

Cf. A075422.

Sequence in context: A038787 A144098 A259140 * A250269 A193987 A089423

Adjacent sequences: A075068 A075069 A075070 * A075072 A075073 A075074

Keyword

nice,nonn

Author

Amarnath Murthy, Sep 09 2002

Extensions

Edited by Robert G. Wilson v, Sep 14 2002

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

Status

approved