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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 ≤ iu.


Find S(1 000 000) mod 1018.