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A375187
Number of unitary square divisors of n!.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 03 2024
STATUS
approved