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/xn

where xi is a strictly increasing sequence of positive integers?

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

© Copyright 2006 Stan Wagon. Reproduced with permission.

10 October 2006