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

0,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Sequence in context: A007407 A051418 A069046 * A069053 A193282 A192217

Adjacent sequences: A065883 A065884 A065885 * A065887 A065888 A065889

Keyword

nonn

Author

Henry Bottomley, Nov 27 2001

Status

approved