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Product of non-unitary divisors of binomial(n, floor(n/2)) or a(n) = 1 if all divisors are unitary. See A046098.
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%I #7 Jul 22 2024 15:23:50

%S 1,1,1,1,1,20,1,1,15876,1016255020032,1,728933458176,8670998958336,

%T 19247673071478783248355557376,1714723915100625,

%U 752711194884611945703392100000000,1,31226235883841773375939805209600000000,1,1357651828905889565182743230460164655087616

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

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

%t 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 *)

%o (PARI) a(n) = apply(x -> x^((numdiv(x) - 2^omega(x))/2), binomial(n, n\2)); \\ _Amiram Eldar_, Jul 22 2024

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

%K nonn

%O 1,6

%A _Labos Elemer_, Sep 13 2001

%E a(18)-a(20) from _Amiram Eldar_, Jul 22 2024