MathNet 2000 — Math Olympiad Vault Question 49

Let $a_{1}, a_{2}, \ldots, a_{n}$ be an arithmetic progression of integers such that $i$ divides $a_{i}$ for $i=1,2, \ldots, n-1$ and $n$ does not divide $a_{n}$. Prove that $n$ is a power of a prime.