OFFSET
1,4
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..500
FORMULA
EXAMPLE
For n=6, 6! = 720 = 144*5 so a(6) = sqrt(144) = 12.
MAPLE
a:= proc(n)
local r, F, t;
r:= n!;
F:= ifactors(r)[2];
mul(t[1]^floor(t[2]/2), t=F)
end proc:
seq(a(n), n= 1 .. 100); # Robert Israel, Oct 19 2014
MATHEMATICA
Table[Last[Select[Sqrt[#]&/@Divisors[n!], IntegerQ]], {n, 30}] (* Harvey P. Dale, Oct 08 2012 *)
(Sqrt@Factorial@Range@30)/.Sqrt[_]->1 (* Morgan L. Owens, May 04 2016 *)
f[p_, e_] := p^Floor[e/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 40] (* Amiram Eldar, Jul 26 2024 *)
PROG
(PARI) a(n)=core(n!, 2)[2] \\ Charles R Greathouse IV, Apr 03 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 12 2000
STATUS
approved