A number theory problem by Benedict Dimacutac

For every positive integer n n , let s ( n ) s(n) denote the number of terminal zeroes in the decimal representation of n!. For example, 10 ! = 3 , 628 , 800 10! = 3, 628, 800 ends in two zeroes, so s ( 10 ) = 2 s(10) = 2 . How many positive integers less than or equal to 2016 2016 cannot be expressed in the form n + s ( n ) n + s(n) for some positive integer n n ?


The answer is 401.

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