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%I #29 May 17 2016 12:09:41
%S 1,1,1,2,2,12,12,24,72,720,720,1440,1440,10080,30240,120960,120960,
%T 725760,725760,7257600,7257600,79833600,79833600,958003200,4790016000,
%U 62270208000,186810624000,2615348736000,2615348736000,15692092416000
%N Square root of largest square dividing n!.
%H Charles R Greathouse IV, <a href="/A055772/b055772.txt">Table of n, a(n) for n = 1..500</a>
%F a(n) = A000188(n!) = sqrt(A008833(n!)) = sqrt(A055071(n)).
%F n! = a(n)^2*A055204(n) = a(n)^2*A007913(n!).
%F n! = (A000188(n!)^2)*A055229(n!)*A055231(n!).
%F log(a(n)) ~ n*log(n)/2. - _David Radcliffe_, Oct 17 2014
%e For n=6, 6!=720=144*5 so a(6)=sqrt(144)=12.
%p a:= proc(n)
%p local r,F,t;
%p r:= n!;
%p F:= ifactors(r)[2];
%p mul(t[1]^floor(t[2]/2),t=F)
%p end proc:
%p seq(a(n), n= 1 .. 100); # _Robert Israel_, Oct 19 2014
%t Table[Last[Select[Sqrt[#]&/@Divisors[n!],IntegerQ]],{n,30}] (* _Harvey P. Dale_, Oct 08 2012 *)
%t (Sqrt@Factorial@Range@30)/.Sqrt[_]->1 (* _Morgan L. Owens_, May 04 2016 *)
%o (PARI) a(n)=core(n!,2)[2] \\ _Charles R Greathouse IV_, Apr 03 2012
%Y Cf. A000188, A008833, A007913, A055229, A055231, A055071, A055204, A055230.
%K nonn
%O 1,4
%A _Labos Elemer_, Jul 12 2000
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