VOOZH about

URL: https://oeis.org/A065886

⇱ A065886 - OEIS

login
A065886
Smallest square divisible by n!.
3
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
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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Nov 27 2001
STATUS
approved