Maximum number of divisors

Let d(n) be the number of divisors of n. Let M(n,k) be the maximum value of d(j) for n ≤ j ≤ n+k-1. Let S(u,k) be the sum of M(n,k) for 1 ≤ n ≤ u-k+1.

You are given that S(1000,10)=17176.

Find S(100 000 000,100 000).

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