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549. Divisibility of factorials

The smallest number m such that 10 divides m! is m=5.
The smallest number m such that 25 divides m! is m=10.

Let s(n) be the smallest number m such that n divides m!.
So s(10)=5 and s(25)=10.
Let S(n) be ∑s(i) for 2 ≤ i ≤ n.
S(100)=2012.

Find S(10⁸).