Problem

Source:

Tags: floor function, calculus, algebra unsolved, algebra



$f(x)=\sum\limits_{i=1}^{2013}\left[\dfrac{x}{i!}\right]$. A integer $n$ is called good if $f(x)=n$ has real root. How many good numbers are in $\{1,3,5,\dotsc,2013\}$?