Let $\varphi(n)$ be Euler's totient function.
Let $f(n)=(\sum_{i=1}^{n}\varphi(n^i)) \bmod (n+1)$.
Let $g(n)=\sum_{i=1}^{n} f(i)$.
$g(100)=2007$.
Find $g(5 \times 10^8)$.
Solution
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