Pairwise Relative Primality of Positive Integers

Given a graph $G=(V,E)$ with $V=\{1,2,\mathrm{.}\mathrm{.}\mathrm{.},k\}$, the $k$ positive integers $a_1,a_2,\mathrm{.}\mathrm{.}\mathrm{.},a_k$ are $G$-wise relatively prime if $(a_i,a_j)=1$ for ${i,j} \in E$\mathrm{.}Inthisnoteweconsidertheproblemoffindingtheprobability$A_G$thatkpositiveintegersare$G$-wise relatively prime. As an application of our results, we solve the problems of finding probabilities that k positive integers have exact (or at least) r relatively prime pairs, which was proposed by P. Moree.