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A055071
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Largest square dividing n!.
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12
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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
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history;
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internal format)
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OFFSET
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1,4
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LINKS
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FORMULA
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MAPLE
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seq(expand(numtheory[nthpow](n!, 2)), n=1..26); # Peter Luschny, Apr 03 2013
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MATHEMATICA
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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 *)
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PROG
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(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())
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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