%I #35 Jul 27 2024 11:14:21
%S 1,1,1,4,4,144,144,576,5184,518400,518400,2073600,2073600,101606400,
%T 914457600,14631321600,14631321600,526727577600,526727577600,
%U 52672757760000,52672757760000,6373403688960000,6373403688960000,917770131210240000,22944253280256000000
%N Largest square dividing n!.
%H Charles R Greathouse IV, <a href="/A055071/b055071.txt">Table of n, a(n) for n = 1..500</a>
%F a(n) = A008833(n!).
%F log a(n) ~ n log n. - _Charles R Greathouse IV_, Apr 04 2012
%F a(n) = A055772(n)^2. - _Amiram Eldar_, Jul 26 2024
%p seq(expand(numtheory[nthpow](n!, 2)), n=1..26); # _Peter Luschny_, Apr 03 2013
%t a[n_] := Select[Reverse @ Divisors[n!], IntegerQ[Sqrt[#]] &, 1] // First; a /@ Range[23] (* _Jean-François Alcover_, May 19 2011 *)
%t f[p_, e_] := p^(2*Floor[e/2]); a[n_] := Times @@ (f @@@ FactorInteger[n!]); Array[a, 30] (* _Amiram Eldar_, Jul 26 2024 *)
%o (PARI) a(n)=core(n!,2)[2]^2 \\ _Charles R Greathouse IV_, Apr 04 2012
%o (Python)
%o from math import prod
%o from itertools import count, islice
%o from collections import Counter
%o from sympy import factorint
%o def A055071_gen(): # generator of terms
%o c = Counter()
%o for i in count(1):
%o c += Counter(factorint(i))
%o yield prod(p**(e-(e&1)) for p, e in c.items())
%o A055071_list = list(islice(A055071_gen(),30)) # _Chai Wah Wu_, Jul 27 2024
%Y Cf. A000188, A008833, A055772.
%K nonn
%O 1,4
%A _Labos Elemer_, Jun 13 2000
%E More terms from _James A. Sellers_, Jun 20 2000