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Sum of largest prime factors

Published on Saturday, 10th November 2018, 04:00 pm; Solved by 245;
Difficulty rating: 45%

Problem 642

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

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