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%I #10 Sep 24 2018 16:53:14
%S 1,3,2,10,60,420,28,252,2520,27720,66,858,12012,180180,2882880,
%T 49008960,882161280,16761064320,8398,176358,3879876,89237148,
%U 2141691552,53542288800,1392099508800,37586686737600,1052427228652800
%N Smallest integer value of n!/(2!3!...p!), where denominator contains product of factorials of primes in increasing order.
%C n!/{prime(1)!*prime(2)!*prime(3)!...*prime(k)!} where k is the largest integer such that {prime(1)!*prime(2)!*prime(3)!...*prime(k)!} divides n!.
%e a(8) = 8!/2!3!5! = 28, as 28/7! is not an integer.
%e a(12) = 12!/{2!*3!*5!*7!} = 66.
%t f[n_] := Block[{k = 1}, While[ IntegerQ[ n!/Product[ Prime[i]!, {i, k}]], k++ ]; n!/Product[Prime[i]!, {i, k - 1}]]; Table[ f[n], {n, 2, 28}] (* _Robert G. Wilson v_, Jun 21 2004 *)
%Y Similar to but different from A074199.
%K nonn
%O 2,2
%A _Amarnath Murthy_, Sep 30 2003
%E More terms from _Ray Chandler_, Oct 06 2003
%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 08 2007
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