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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