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%I #22 Dec 10 2014 06:15:23
%S 1,1,2,6,3,15,5,35,70,70,7,77,231,3003,858,1430,1430,24310,12155,
%T 230945,46189,230945,176358,4056234,676039,676039,104006,312018,44574,
%U 1292646,1077205,33393355,66786710,2203961430,64822395,90751353,90751353,3357800061,353452638,1531628098,3829070245,156991880045
%N n!/pp, where pp is the largest perfect power (A001597) which divides n!.
%H Robert G. Wilson v, <a href="/A251753/b251753.txt">Table of n, a(n) for n = 0..100</a>
%F If p is prime, then a(p) = p*a(p-1).
%F a(n) = n! / A090630(n). - _Joerg Arndt_, Dec 08 2014
%t perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; f[n_] := Block[{d = Divisors[n!], k = 1}, While[ ! perfectPowerQ[ d[[-k]]], k++]; n!/d[[-k]]]; Array[f, 41, 0] (* or *)
%t f[n_] := Block[{fi = FactorInteger[n!]}, n!/Times @@ (#1[[1]] ^ (2 Quotient[#1[[2]],2])&) /@ fi]; f[4] = 3; f[5] = 15; f[21] = 230945; Array[f, 40]
%Y Cf. A000142, A001597, A090630.
%K nonn
%O 0,3
%A _Robert G. Wilson v_, Dec 07 2014
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