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).

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