# Log-splitting with Chris

Algebra Level pending

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.

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