MathNet 2015-part-04 — 191 problems (EN–VI) Question 30

Find all positive integers $n$ such that there exists a positive integer with $n^2$ divisors (including $1$ and itself) and an arrangement of those divisors (each divisor is used once) in an $n \times n$ grid, where the sum of the divisors in each row and column is the same.

(Battsengel B., Bayarmagnai G.)