Problem 320
Factorials divisible by a huge integer

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.

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http://projecteuler.net/problem=320