Question 50
Let $f(x) = \lfloor \frac{x}{1!} \rfloor + \lfloor \frac{x}{2!} \rfloor + \dots + \lfloor \frac{x}{2013!} \rfloor$, where $\lfloor x \rfloor$ is the greatest integer no greater than $x$. Call an integer $n$ a good number if the equation $f(x) = n$ has a real solution $x$. Find the number of good numbers in the set $\{1, 3, 5, \dots, 2013\}$.