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A376556
The number of non-unitary square divisors of binomial(n, floor(n/2)).
5
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 4, 6, 2, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 6, 8, 0, 0, 0, 4, 4, 6, 2, 2, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 4, 4, 0, 0, 4, 8, 2, 3, 6, 8
OFFSET
0,27
LINKS
FORMULA
a(n) = A056626(A001405(n)).
MATHEMATICA
f1[p_, e_] := 1 + Floor[e/2]; f2[p_, e_] := 2^(1 - Mod[e, 2]); a[0] = a[1] = 0; a[n_] := Times @@ f1 @@@ (fct = FactorInteger[Binomial[n, Floor[n/2]]]) - Times @@ f2 @@@ fct; Array[a, 60, 0]
PROG
(PARI) a(n) = {my(e = factor(binomial(n, n\2))[, 2]); vecprod(apply(x -> x\2 + 1, e)) - vecprod(apply(x -> 1 << (1 - x%2), e)); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 28 2024
STATUS
approved