Enhanced perfect power
Public  11/06/17  9xp  Math  47.6% 
A perfect power $n$ is called enhanced if there exists two integers $m>0$ and $k>2$ such that $n=m^k$. The enhanced perfect powers no more than $100$ are $1, 8, 16, 27, 32, 64, 81$.
Let $S(N)$ be the sum of all enhanced perfect powers no more than $N$. You are given $S(100) = 229$, $S(10000) = 99352$ and $S(10^8) \mod 1000000007 = 553225565$.
Find $S(10^{100}) \mod 1000000007$.
Let $S(N)$ be the sum of all enhanced perfect powers no more than $N$. You are given $S(100) = 229$, $S(10000) = 99352$ and $S(10^8) \mod 1000000007 = 553225565$.
Find $S(10^{100}) \mod 1000000007$.
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