Question 62
Let $a_1, a_2, a_3, a_4$ be positive integers such that in any circular arrangement of these numbers there are two adjacent non-coprime ones. What is the maximal possible number of ordered triples $(i, j, k)$; $i, j, k \in \{1, 2, 3, 4\}$ and $i \neq j, j \neq k, k \neq i$, such that $(\text{gcd}(a_i, a_j))^2 \mid a_k$?