The probability that \(k\) positive integers are pairwise relatively prime (Q2785023)

The probability that \(k\) positive integers chosen at random are relatively prime is \(\prod_p (1-\frac{1}{p^k})= \frac{1}{\zeta(k)}\) [\textit{J. E. Nymann}, J. Number Theory 4, 469-473 (1972; Zbl 0246.10038)]. The author shows that the probability that \(k\) positive integers are pairwise relatively prime is \(\prod_p (1-\frac{1}{p})^{k-1} (1+ \frac{k-1}{p})\). He even proves a sharper asymptotic formula.