Factorials divisible by a huge integer (noch nicht übersetzt)

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.