CGMO 2005 Problem 7

Let $m$ and $n$ be positive integers with $m > n \geq 2.$ Set $S = \{1, 2, \ldots, m\},$ and $T = \{a_l, a_2, \ldots, a_n\}$ is a subset of S such that every number in $S$ is not divisible by any two distinct numbers in $T.$ Prove that $$\sum^n_{i = 1} \frac {1}{a_i} < \frac {m + n}{m}.$$