Amazingly advanced

p ( n ) = k = 1 y n 5 k p(n) = \sum _{ k=1 }^{ y }{ \left\lfloor \frac { n }{ { 5 }^{ k } } \right\rfloor }

Given n , y , k n,y,k are positive integers, y y is the largest integer such that the inequality 5 y n 5^y \leq n is satisfied. For the function p ( n ) p(n) as described above, if p ( n ) = 781 p(n) = 781 . Find the sum of all possible values of n n .


The answer is 15635.

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