Question 28
Determine all increasing sequence $a_1, a_2, a_3, \ldots$ of positive integers such that for every $i, j \in \mathbb{N}$, the number of positive divisors of $i + j$ and $a_i + a_j$ are equal (A sequence $a_1, a_2, a_3, \ldots$ is increasing if $i \le j$ implies $a_i \le a_j$).