Question 95
Find all positive integers $n$ for which there exist $n$ distinct natural numbers $a_{1}, a_{2}, \ldots, a_{n}$, none of them greater than $n^{2}$, such that the sum
$$
\frac{1}{a_{1}}+\frac{1}{a_{2}}+\cdots+\frac{1}{a_{n}}=1.
$$
$$
\frac{1}{a_{1}}+\frac{1}{a_{2}}+\cdots+\frac{1}{a_{n}}=1.
$$