Largest prime factors of consecutive numbers (noch nicht übersetzt)

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).