A065886 Smallest square divisible by n!.

1, 1, 4, 36, 144, 3600, 3600, 176400, 2822400, 25401600, 25401600, 3073593600, 110649369600, 18699743462400, 74798973849600, 1869974346240000, 29919589539840000, 8646761377013760000, 77820852393123840000, 28093327713917706240000, 112373310855670824960000

Offset: 0

Author

Henry Bottomley, Nov 27 2001

Keywords

• nonn

Examples

			a(10) = 25401600 since 10! = 3628800 and the smallest square divisible by this is 25401600 = 3628800*7 = 5040^2
		

Links

• Robert Israel, Table of n, a(n) for n = 0..407

Programs

Maple

N:= 50: # to get a(0)..a(N)
P:= select(isprime, [$2..N]):
nP:= nops(P):
V:= Vector(nP):
A[0]:= 1:
for n from 1 to N do
  for i from 1 to nP do V[i]:= V[i] + padic:-ordp(n,P[i]) od;
  A[n]:= mul(P[i]^(2*ceil(V[i]/2)),i=1..nP)
od:
seq(A[n],n=0..N); # Robert Israel, Jan 30 2017

Mathematica

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 *)

Formula

a(n) = A053143(A000142(n)) = A065887(n)^2 = A000142(n)*A055204(n) = A001044(n)/A055071(n)