MathNet 2003 — Part 02 Question 92

For every positive integer $n \geq 1$ we define the matrix $A_n = (a_{ij})_{1 \leq i, j \leq n}$, where $a_{ij} = \max(i, j) / \min(i, j)$, $1 \leq i, j \leq n$. Calculate the determinant of the matrix $A_n$.