Question 11
Let $n$ be an integer, $n \ge 2$. For each $k = 1, 2, \dots, n$, let $a_k$ be the number of multiples of $k$ in the set $\{1, 2, \dots, n\}$, and let $x_k = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{a_k}$. Show that $\frac{x_1 + x_2 + \dots + x_n}{n} \le \frac{1}{1^2} + \frac{1}{2^2} + \dots + \frac{1}{n^2}$.