GCD(k,j) Product

[Leroy Quet]

Analogous to sequence A018806, but with the double sum replaced with a 
double product,

we can have the sequence:

a(n) =


product{k=1 to n} product{j=1 to n}  GCD(k,j),

which begins, I believe:

1, 2, 6, 96, 480,...,

which is not in the EIS.


Am I right to assume that:

limit{n-> oo}  a(n)^(1/n^2) =

exp(-zeta'(2)/zeta(2)) ?

(where zeta(2) = pi^2/6,
and zeta'(2) is the derivative of the Riemann zeta function at 2)


thanks,
Leroy Quet