# Problem 320: Factorials divisible by a huge integer

![graphic](img320.gif)

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 1018.