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Problem 642

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Sum of largest prime factors

Let $f(n)$ be the largest prime factor of $n$ and $F(n)=\sum _{i=2}^{n}f(i)$.
For example $F(10)=32$, $F(100)=1915$ and $F(10000)=10118280$.

Find $F(201820182018)$. Give your answer modulus ${10}^9$.

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最大质因数之和

记$f(n)$为$n$的最大质因数，并记$F(n)=\sum _{i=2}^{n}f(i)$。
已知$F(10)=32$，$F(100)=1915$，$F(10000)=10118280$。

求$F(201820182018)$，并将你的答案对${10}^9$取余.

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