0%

Problem 526


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)。