Question 58
Given a positive integer $n$, find the smallest value of
$$
\left\lfloor\frac{a_{1}}{1}\right\rfloor+\left\lfloor\frac{a_{2}}{2}\right\rfloor+\cdots+\left\lfloor\frac{a_{n}}{n}\right\rfloor
$$
over all permutations $(a_{1}, a_{2}, \ldots, a_{n})$ of $(1,2, \ldots, n)$.
$$
\left\lfloor\frac{a_{1}}{1}\right\rfloor+\left\lfloor\frac{a_{2}}{2}\right\rfloor+\cdots+\left\lfloor\frac{a_{n}}{n}\right\rfloor
$$
over all permutations $(a_{1}, a_{2}, \ldots, a_{n})$ of $(1,2, \ldots, n)$.