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

0,7

Comments

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

Links

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

Formula

a(n) = A056624(n!).

Mathematica

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

Prog

(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<<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

Crossrefs

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

Sequence in context: A002581 A161778 A099655 * A276149 A146899 A317726

Adjacent sequences: A375184 A375185 A375186 * A375188 A375189 A375190

Keyword

nonn,easy

Author

Amiram Eldar, Aug 03 2024

Status

approved