MathNet 2016-part-02 — 184 problems (EN–VI) Question 184

Determine all sequences of non-negative integers $a_{1}, \ldots, a_{2016}$ all less than or equal to $2016$ satisfying $i+j \mid i a_{i}+j a_{j}$ for all $i, j \in \{1,2, \ldots, 2016\}$.