MathNet 2022-part-06 — 196 problems (EN–VI) Question 70

Let $f$ be a function from $\{1,2, \ldots, 22\}$ to the positive integers such that $m n \mid f(m)+f(n)$ for all $m, n \in \{1,2, \ldots, 22\}$. If $d$ is the number of positive divisors of $f(20)$, compute the minimum possible value of $d$.
Proposed by: Sheldon Kieren Tan