cp's OEIS Frontend

A375187 Number of unitary square divisors of n!.

%I A375187 #16 Aug 07 2024 09:14:42
%S A375187 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 A375187 32,16,4,16,16,16,16,16,16,16,16,8,8,16,32,128,128,256,256,128,32,64,
%U A375187 64,256,64,16,4,16,16,64,64,64,128,128,32,64,64,128,128
%N A375187 Number of unitary square divisors of n!.
%C A375187 Unitary analog of A046951(n!) = A055993(n).
%H A375187 Amiram Eldar, <a href="/A375187/b375187.txt">Table of n, a(n) for n = 0..1000</a>
%F A375187 a(n) = A056624(n!).
%t A375187 f[p_, e_] := 2^(1 - Mod[e, 2]); a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 100, 0]
%o A375187 (PARI) a(n) = vecprod(apply(x -> 1 << (1 - x%2), factor(n!)[,2]));
%o A375187 (Python)
%o A375187 from collections import Counter
%o A375187 from sympy import factorint
%o A375187 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 A375187 Cf. A000142, A046951, A055993, A056624, A375188.
%K A375187 nonn,easy
%O A375187 0,7
%A A375187 _Amiram Eldar_, Aug 03 2024