A064033 Product of non-unitary divisors of binomial(n, floor(n/2)) or a(n) = 1 if all divisors are unitary. See A046098.

1, 1, 1, 1, 1, 20, 1, 1, 15876, 1016255020032, 1, 728933458176, 8670998958336, 19247673071478783248355557376, 1714723915100625, 752711194884611945703392100000000, 1, 31226235883841773375939805209600000000, 1, 1357651828905889565182743230460164655087616

Offset

1,6

Links

Table of n, a(n) for n=1..20.

Formula

a(n) = A061538(A001405(n)).

Mathematica

f[n_] := n^((DivisorSigma[0, n] - 2^PrimeNu[n]) / 2); Table[f[Binomial[n, Floor[n/2]]], {n, 1, 20}] (* Amiram Eldar, Jul 22 2024 *)

Prog

(PARI) a(n) = apply(x -> x^((numdiv(x) - 2^omega(x))/2), binomial(n, n\2)); \\ Amiram Eldar, Jul 22 2024

Crossrefs

Cf. A001405, A048243, A056173, A061537, A061538.

Sequence in context: A257608 A022183 A015146 * A040409 A040408 A040407

Adjacent sequences: A064030 A064031 A064032 * A064034 A064035 A064036

Keyword

nonn

Author

Labos Elemer, Sep 13 2001

Extensions

a(18)-a(20) from Amiram Eldar, Jul 22 2024

Status

approved