The Hafner-Sarnak-McCurley constant $\omega$ is the limit of the probabilities $D(n)$ as $n \to \infty$ that the determinants of two random $n\times n$ matrices with integral coefficients have coprime determinants.
Formulas
(1)
$\omega = \prod_p \big(1- \big(1 - \prod_{j=1}^\infty (1-p^{-j})\big)^2 \big)$, where the outer product ranges over all primes $p$.
L. Hafner, P. Sarnak and K. McCurley, "Relatively prime values of polynomials", In A Tribute to Emil Grosswald: Number Theory and Related Analysis, Contemporary Mathematics (1993), M. Knopp and M. Sheigorn, Editors, vol. 143.
