Problem of the Week 1061

A Fractional Sum

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

1/x₁ + 2/x₂ + 3/x₃ + ... + 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.