Question 66
Let $n$ be a given positive integer, and let $a_1, a_2, \dots, a_n$ be a permutation of $1, 2, \dots, n$. Determine the minimum value of $\sum_{i=1}^{n} \lfloor \frac{a_i}{i} \rfloor$.
Note: $\lfloor x \rfloor$ denotes the largest integer not exceeding the real number $x$.
Note: $\lfloor x \rfloor$ denotes the largest integer not exceeding the real number $x$.