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Sums of totients of powers

Published on Saturday, 18th April 2015, 10:00 pm; Solved by 1219;
Difficulty rating: 25%

Problem 512

Let $\varphi(n)$ be Euler's totient function.

Let $f(n)=(\sum_{i=1}^{n}\varphi(n^i)) \text{ mod } (n+1)$.

Let $g(n)=\sum_{i=1}^{n} f(i)$.

$g(100)=2007$.

Find $g(5 \times 10^8)$.