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 $10^{9}$ .

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.