ToT 2005-fall SA1

For which $n \ge 2$ can one find a sequence of distinct positive integers $a_1, a_2, \ldots , a_n$ so that the sum $$\frac{a_1}{a_2} + \frac{a_2}{a_3} + \ldots +\frac{a_n}{a_1}$$ is an integer?

(3 points)