A374989 - OEIS

%I #14 Jul 27 2024 12:33:09

%S 1,1,1,1,1,1,12,12,3,9,720,720,160,160,35,189,189,189,145152,145152,

%T 7257600,12800,275,275,136857600,684288000,4343625,17875,875875,

%U 875875,125536739328,125536739328,15324309,637,709689344,9052160000,18104320000,18104320000,2624375

%N Square root of largest unitary square divisor of n!.

%C Unitary analog of A055772.

%C a(n) is even if and only if n > 1 and is in A006364.

%H Amiram Eldar, <a href="/A374989/b374989.txt">Table of n, a(n) for n = 0..1118</a>

%F a(n) = sqrt(A374988(n)).

%F a(n) = A071974(n!).

%t f[p_, e_] := If[EvenQ[e], p^(e/2), 1]; a[0] = a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 40, 0]

%o (PARI) a(n) = {my(f = factor(n!)); prod(i = 1, #f~, if(f[i, 2]%2, 1, f[i, 1]^(f[i, 2]/2)));}

%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 A374989_gen(): # generator of terms

%o     c = Counter()

%o     for i in count(0):

%o         c += Counter(factorint(i))

%o         yield prod(p**(e>>1) for p, e in c.items() if e&1^1)

%o A374989_list = list(islice(A374989_gen(),30)) # _Chai Wah Wu_, Jul 27 2024

%Y Cf. A006364, A055772, A071974, A374988.

%K nonn

%O 0,7

%A _Amiram Eldar_, Jul 26 2024