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Problem 485

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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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约数的最大数目

记d(n)是n的约数的数目。
记M(n,k)是对于n ≤ j ≤ n+k-1，d(j)的最大值。
记S(u,k)是对于1 ≤ n ≤ u-k+1，M(n,k)的和。

已知S(1000,10)=17176。

求S(100 000 000,100 000)。

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