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Divisibility comparison between factorials

Problem 383

Published on Saturday, 5th May 2012, 11:00 pm; Solved by 318

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)!) < 2·f5(i!) and 1 ≤ in.
It can be verified that T5(103) = 68 and T5(109) = 2408210.

Find T5(1018).