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A376555
The number of unitary square divisors of binomial(n, floor(n/2)).
5
1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 4, 2, 4, 2, 2, 4, 2, 2, 1, 2, 2, 4, 4, 2, 2, 4, 2, 1, 2, 1, 2, 4, 4, 8, 8, 4, 4, 2, 2, 4, 2, 1, 1, 2, 1, 2, 2, 1, 4, 4, 2, 4, 2, 4, 4, 2, 1, 2, 2, 1, 4, 2, 4, 8, 2, 4, 8, 4, 2, 1, 2, 4
OFFSET
0,7
LINKS
FORMULA
a(n) = A056624(A001405(n)).
MATHEMATICA
f[p_, e_] := 2^(1 - Mod[e, 2]); a[n_] := Times @@ f @@@ FactorInteger[Binomial[n, Floor[n/2]]]; Array[a, 100, 0]
PROG
(PARI) a(n) = vecprod(apply(x -> 1 << (1 - x%2), factor(binomial(n, n\2))[, 2]));
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 28 2024
STATUS
approved