## Factorials divisible by a huge integer

### Problem 320

Published on Saturday, 15th January 2011, 10:00 pm; Solved by 495; Difficulty rating: 50%
Let N(`i`) be the smallest integer `n` such that `n`! is divisible by (`i`!)^{1234567890}

Let S(`u`)=∑N(`i`) for 10 ≤ `i` ≤ `u`.

S(1000)=614538266565663.

Find S(1 000 000) mod 10^{18}.