It's trailing zeroes again!

Number Theory Level pending

Let us define the function \(\psi (n)\) as the number of trailing zeroes in \(n!\). For example \(\psi (100)=24\) because the number of trailing zeroes at the end of \(100!\) is \(24\).

Problem:

Find the sum of all \(n\) such that \(\psi (n)=2017\)

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