Let $n$ be an integer, $n \ge 2$. For each number $k = 1, 2, ....., n,$ denote by $a _ k$ the number of multiples of $k$ in the set $\{1, 2,. .., n \}$ and let $x _ k = \frac {1} {1} + \frac {1} {2} + \frac {1} {3} _... + \frac {1} {a _ k}$ . Show that: $$\frac {x _ 1 + x _ 2 + ... + x _ n} {n} \le \frac {1} {1 ^ 2} + \frac {1} {2 ^ 2} + ... + \frac {1} {n ^ 2} $$.