Permutations Through Number Theory

Let $a_n$ be the number of permutations $(x_1, x_2, \dots, x_n)$ of the numbers $(1,2,\dots, n)$ such that the $n$ ratios $\frac {x_k}{k}$ for $1 \le k \le n$ are all distinct.

What value can $\large\ a_n$ , $n \ge 1$ take ?