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A055071
Largest square dividing n!.
12
1, 1, 1, 4, 4, 144, 144, 576, 5184, 518400, 518400, 2073600, 2073600, 101606400, 914457600, 14631321600, 14631321600, 526727577600, 526727577600, 52672757760000, 52672757760000, 6373403688960000, 6373403688960000, 917770131210240000, 22944253280256000000
OFFSET
1,4
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..500
FORMULA
a(n) = A008833(n!).
log a(n) ~ n log n. - Charles R Greathouse IV, Apr 04 2012
a(n) = A055772(n)^2. - Amiram Eldar, Jul 26 2024
MAPLE
seq(expand(numtheory[nthpow](n!, 2)), n=1..26); # Peter Luschny, Apr 03 2013
MATHEMATICA
a[n_] := Select[Reverse @ Divisors[n!], IntegerQ[Sqrt[#]] &, 1] // First; a /@ Range[23] (* Jean-François Alcover, May 19 2011 *)
f[p_, e_] := p^(2*Floor[e/2]); a[n_] := Times @@ (f @@@ FactorInteger[n!]); Array[a, 30] (* Amiram Eldar, Jul 26 2024 *)
PROG
(PARI) a(n)=core(n!, 2)[2]^2 \\ Charles R Greathouse IV, Apr 04 2012
(Python)
from math import prod
from itertools import count, islice
from collections import Counter
from sympy import factorint
def A055071_gen(): # generator of terms
c = Counter()
for i in count(1):
c += Counter(factorint(i))
yield prod(p**(e-(e&1)) for p, e in c.items())
A055071_list = list(islice(A055071_gen(), 30)) # Chai Wah Wu, Jul 27 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 13 2000
EXTENSIONS
More terms from James A. Sellers, Jun 20 2000
STATUS
approved