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A374988 Largest unitary square divisor of n!.

%I A374988 #14 Jul 27 2024 15:56:34
%S A374988 1,1,1,1,1,1,144,144,9,81,518400,518400,25600,25600,1225,35721,35721,
%T A374988 35721,21069103104,21069103104,52672757760000,163840000,75625,75625,
%U A374988 18730002677760000,468250066944000000,18867078140625,319515625,767157015625,767157015625,15759472921106221891584
%N A374988 Largest unitary square divisor of n!.
%C A374988 Unitary analog of A055071.
%C A374988 a(n) is even if and only if n > 1 and is in A006364.
%H A374988 Amiram Eldar, <a href="/A374988/b374988.txt">Table of n, a(n) for n = 0..673</a>
%F A374988 a(n) = A350388(n!).
%F A374988 a(n) = A374989(n)^2.
%t A374988 f[p_, e_] := If[EvenQ[e], p^e, 1]; a[0] = a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 30, 0]
%o A374988 (PARI) a(n) = {my(f = factor(n!)); prod(i = 1, #f~, if(f[i, 2]%2, 1, f[i, 1]^f[i, 2]));}
%o A374988 (Python)
%o A374988 from math import prod
%o A374988 from itertools import count, islice
%o A374988 from collections import Counter
%o A374988 from sympy import factorint
%o A374988 def A374988_gen(): # generator of terms
%o A374988     c = Counter()
%o A374988     for i in count(0):
%o A374988         c += Counter(factorint(i))
%o A374988         yield prod(p**e for p, e in c.items() if e&1^1)
%o A374988 A374988_list = list(islice(A374988_gen(),30)) # _Chai Wah Wu_, Jul 27 2024
%Y A374988 Cf. A006364, A055071, A350388, A374989.
%K A374988 nonn
%O A374988 0,7
%A A374988 _Amiram Eldar_, Jul 26 2024