lean_workbook_plus_71300

Thus we want the number of $k$ such that $\frac{2013}{k}$ is reduced and satisfies $\frac{1}{1} < \frac{2013}{k} < 1000$ It is easy to see that this holds exactly for $3 \le k < 2013$ , and so we want the number of $k$ coprime to $2013$ in this range. $\phi(2013) = 1200$ , but we don't want to count $k = 1$ and $k = 2$ , so we get $1200 - 2 = 1198$ occurrences of the number $2013$ .