Given a positive integer n, which integers can arise as the following sum

1/x_{1} + 2/x_{2} + 3/x_{3} + ... + n/x_{n}

where x_{i} is a strictly increasing sequence of positive integers?

Source: 13th Irish Olympiad, Crux Mathematicorum May 2006.

© Copyright 2006 Stan Wagon. Reproduced with permission.