%I #16 Aug 07 2024 09:14:42

%S 1,1,1,1,1,1,4,4,2,2,8,8,4,4,4,4,4,4,8,8,16,4,4,4,16,16,16,8,16,16,32,

%T 32,16,4,16,16,16,16,16,16,16,16,8,8,16,32,128,128,256,256,128,32,64,

%U 64,256,64,16,4,16,16,64,64,64,128,128,32,64,64,128,128

%N Number of unitary square divisors of n!.

%C Unitary analog of A046951(n!) = A055993(n).

%H Amiram Eldar, <a href="/A375187/b375187.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A056624(n!).

%t f[p_, e_] := 2^(1 - Mod[e, 2]); a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 100, 0]

%o (PARI) a(n) = vecprod(apply(x -> 1 << (1 - x%2), factor(n!)[,2]));

%o (Python)

%o from collections import Counter

%o from sympy import factorint

%o def A375187(n): return 1<<sum(e&1^1 for e in sum((Counter(factorint(m)) for m in range(2,n+1)),start=Counter()).values()) # _Chai Wah Wu_, Aug 03 2024

%Y Cf. A000142, A046951, A055993, A056624, A375188.

%K nonn,easy

%O 0,7

%A _Amiram Eldar_, Aug 03 2024