MathNet 2015-part-07 — 185 problems (EN–VI) Question 153

Let $\pi$ be a permutation of $\{1,2, \ldots, 2015\}$. With proof, determine the maximum possible number of ordered pairs $(i, j) \in \{1,2, \ldots, 2015\}^{2}$ with $i\lt j$ such that $\pi(i) \cdot \pi(j)\gt i \cdot j$.