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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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%I #21 Mar 24 2024 11:19:35

%S 1,1,1,12,1,60,1,20160,60480,15120,1,39916800,1,8648640,1816214400,

%T 10461394944000,1,533531142144000,1,10137091700736000,

%U 1689515283456000,14079294028800,1,51704033477769953280000,129260083694424883200000,32382376266240000

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

%C 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

%H T. D. Noe, <a href="/A075072/b075072.txt">Table of n, a(n) for n = 1..400</a>

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

%t Table[n!/Times@@(First[Transpose[FactorInteger[n]]]!),{n,30}] (* _Harvey P. Dale_, May 07 2011 *)

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

%K nice,nonn,easy

%O 1,4

%A _Amarnath Murthy_, Sep 09 2002

%E a(26) from _Harvey P. Dale_, May 07 2011