Question 3
Determine which integers $n \gt 1$ have the property
that there exists an infinite sequence $a_1$, $a_2$, $a_3$, …
of nonzero integers such that the equality
\[ a_k + 2a_{2k} + \dots + na_{nk} = 0 \]
holds for every positive integer $k$.
that there exists an infinite sequence $a_1$, $a_2$, $a_3$, …
of nonzero integers such that the equality
\[ a_k + 2a_{2k} + \dots + na_{nk} = 0 \]
holds for every positive integer $k$.