Log-splitting with Chris

For any positive integer $n$ , define

$f(n)= \begin{cases} \log_{4} n & \mbox{ if } \log_4 n \mbox{ is rational}, \\ 0 & \mbox { otherwise}. \\ \end{cases}$

If $\sum\limits_{i=1}^{2013}f(n)$ is expressed as $\frac{a}{b}$ , where $a$ and $b$ are coprime positive integers, what is the value of $a+b$ ?

This problem is posed by Chris C .