MathNet 2022-part-01 — 197 problems (EN–VI) Question 11

Determine the number of permutations $a_1, a_2, \ldots, a_{2021}$ of the numbers $2, 3, \ldots, 2022$ such that $a_k$ is divisible by $k$, for all $k = 1, 2, \ldots, 2021$.