A375187 Number of unitary square divisors of n!.

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

Offset: 0

Author

Amiram Eldar, Aug 03 2024

Keywords

• nonn
• easy

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1000

Crossrefs

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

Programs

Mathematica

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

PARI

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

Python

from collections import Counter
from sympy import factorint
def A375187(n): return 1<Chai Wah Wu, Aug 03 2024

Formula

a(n) = A056624(n!).