Question 132
Determine all integers $n \geqslant 1$ as there is a $(a_{1}, a_{2}, \ldots, a_{n})$ permutation of $(1,2, \ldots, n)$ for the following condition: $$
k \mid a_{1}+a_{2}+\ldots+a_{k}
$$ for all $k \in\{1,2, \ldots, n\}$.
k \mid a_{1}+a_{2}+\ldots+a_{k}
$$ for all $k \in\{1,2, \ldots, n\}$.