MathNet 2015-part-04 — 191 problems (EN–VI) Question 82

Determine all positive integers expressible, for every integer $n \ge 3$, in the form $\frac{(a_1 + 1)(a_2 + 1)\cdots(a_n + 1) - 1}{a_1a_2\cdots a_n}$, where $a_1, a_2, \ldots, a_n$ are pairwise distinct positive integers.