DK-GEORGMOHR 2016 Problem 5

Find all possible values of the number $$\frac{a + b}{c}+\frac{a + c}{b}+\frac{b + c}{a},$$ where $a, b, c$ are positive integers, and $\frac{a + b}{c},\frac{a + c}{b},\frac{b + c}{a}$ are also positive integers.