Problem 526
Largest prime factors of consecutive numbers
Let f(n) be the largest prime factor of n.
Let g(n) = f(n) + f(n+1) + f(n+2) + f(n+3) + f(n+4) + f(n+5) + f(n+6) + f(n+7) + f(n+8), the sum of the largest prime factor of each of nine consecutive numbers starting with n.
Let h(n) be the maximum value of g(k) for 2 ≤ k ≤ n.
You are given:
-f(100) = 5
-f(101) = 101
-g(100) = 409
-h(100) = 417
-h(109) = 4896292593
Find h(1016).
连续数的最大质因数
记f(n)是n的最大质因数。
记g(n) = f(n) + f(n+1) + f(n+2) + f(n+3) + f(n+4) + f(n+5) + f(n+6) + f(n+7) + f(n+8)，即从n开始连续九个数的最大质因数之和。
记h(n)为2 ≤ k ≤ n中g(k)的最大值。
已知：
- f(100) = 5
- f(101) = 101
- g(100) = 409
- h(100) = 417
- h(109) = 4896292593
求h(1016)。