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%I #12 Sep 28 2023 01:59:29
%S 1,2,6,12,120,60,5040,840,60480,15120,39916800,2310,6227020800,
%T 8648640,1816214400,10810800,355687428096000,2042040,
%U 121645100408832000,116396280,1689515283456000,14079294028800,25852016738884976640000
%N 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.
%C 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.
%e a(12) = 12! / (2!*3!*4!*6!) = 2310.
%t Select[Table[ n!/ Apply[ Times, Drop[ Divisors[n], -1]! ], {n, 1, 23}], IntegerQ]
%t Select[Table[n!/Times@@(Most[Divisors[n]]!),{n,30}],IntegerQ] (* _Harvey P. Dale_, Aug 01 2020 *)
%Y Cf. A075422.
%K nice,nonn
%O 1,2
%A _Amarnath Murthy_, Sep 09 2002
%E Edited by _Robert G. Wilson v_, Sep 14 2002
%E First Mathematica program modified by _Harvey P. Dale_, Aug 01 2020
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