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A065886 Smallest square divisible by n!. 2
1, 1, 4, 36, 144, 3600, 3600, 176400, 2822400, 25401600, 25401600, 3073593600, 110649369600, 18699743462400, 74798973849600, 1869974346240000, 29919589539840000, 8646761377013760000, 77820852393123840000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 22 04:29 EDT 2019. Contains 322329 sequences. (Running on oeis4.)