Question 64
Let $n$ be a natural number. Determine the number of permutations $\left(a_{1}, \ldots, a_{n}\right)$ of the set $\{1,2, \ldots, n\}$ with the following property: $$2\left(a_{1}+\ldots+a_{k}\right) \quad \text{ is divisible by } k \quad \forall k \in\{1,2, \ldots, n\}$$