Question 20
Find all positive integer $n$ such that there exists a permutation $\left(a_{1}, a_{2}, \ldots, a_{n}\right)$ of $\left(1,2,3, \ldots, n\right)$ satisfying the condition:
$$
a_{1}+a_{2}+\cdots+a_{k} \text{ is divisible by } k \text{ for each } k=1,2,3, \ldots, n \text{. }
$$
$$
a_{1}+a_{2}+\cdots+a_{k} \text{ is divisible by } k \text{ for each } k=1,2,3, \ldots, n \text{. }
$$