Maximum number of divisors
Problem 485
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.
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).