Question 67
For each integer $n \ge 1$, define $a_n = \lfloor \frac{n}{\sqrt{n}} \rfloor$, where $\lfloor x \rfloor$ denotes the largest integer not exceeding $x$, for any real number $x$. Find the number of all $n$ in the set $\{1, 2, 3, \dots, 2010\}$ for which $a_n \gt a_{n+1}$.