Find all $n\in \mathbb{N}$, $n>1$ with the following property: All divisors of $n$ can be put in a rectangular table in such way that the sums of the numbers by rows are equal and the sums of the numbers by columns are also equal.
Problem
Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade
Tags: number theory, numbers in a table