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A065886 Smallest square divisible by n!.

%I A065886 #11 Jan 24 2022 17:28:08
%S A065886 1,1,4,36,144,3600,3600,176400,2822400,25401600,25401600,3073593600,
%T A065886 110649369600,18699743462400,74798973849600,1869974346240000,
%U A065886 29919589539840000,8646761377013760000,77820852393123840000,28093327713917706240000,112373310855670824960000
%N A065886 Smallest square divisible by n!.
%H A065886 Robert Israel, <a href="/A065886/b065886.txt">Table of n, a(n) for n = 0..407</a>
%F A065886 a(n) = A053143(A000142(n)) = A065887(n)^2 = A000142(n)*A055204(n) = A001044(n)/A055071(n)
%e A065886 a(10) = 25401600 since 10! = 3628800 and the smallest square divisible by this is 25401600 = 3628800*7 = 5040^2
%p A065886 N:= 50: # to get a(0)..a(N)
%p A065886 P:= select(isprime, [$2..N]):
%p A065886 nP:= nops(P):
%p A065886 V:= Vector(nP):
%p A065886 A[0]:= 1:
%p A065886 for n from 1 to N do
%p A065886   for i from 1 to nP do V[i]:= V[i] + padic:-ordp(n,P[i]) od;
%p A065886   A[n]:= mul(P[i]^(2*ceil(V[i]/2)),i=1..nP)
%p A065886 od:
%p A065886 seq(A[n],n=0..N); # _Robert Israel_, Jan 30 2017
%t A065886 ssd[n_]:=Module[{nf=n!,k=1},While[!IntegerQ[Sqrt[k*nf]],k++];k*nf]; Array[ssd,20,0] (* _Harvey P. Dale_, Apr 29 2012 *)
%K A065886 nonn
%O A065886 0,3
%A A065886 _Henry Bottomley_, Nov 27 2001