Question 34
Find the largest positive integer $n$ for which there exists a set $\{a_{1}, a_{2}, \ldots, a_{n}\}$ of composite positive integers with the following properties:
(i) any two of them are coprime;
(ii) $1 \lt a_{i} \leq (3n+1)^{2}$ for $i = 1, \ldots, n$.
(i) any two of them are coprime;
(ii) $1 \lt a_{i} \leq (3n+1)^{2}$ for $i = 1, \ldots, n$.