Problem 383
Divisibility comparison between factorials

Let f5(n) be the largest integer x for which 5x divides n.
For example, f5(625000) = 7.

Let T5(n) be the number of integers i which satisfy f5((2·i-1)!) 5(i!) and 1 ≤i ≤n.
It can be verified that T5(103) = 68 and T5(109) = 2408210.

Find T5(1018).

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK