Zeroes After a Factorial

Let \(f(n,k)\) be the number of zeroes at the end of \(n!\) in base \(k\).

Let \(g(r)=f(r,2)+f(r,3)+f(r,4)+...+f(r,r)\)

Find \(g(100)\)

----- Examples -----

\(f(100,10)=24\)

\(f(53, 7)=8\)

\(f(5,16)=0\)

\(g(7)=12\)

\(g(25)=136\)

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