Logarithm of the Factorial Pt 2

\[\large{ f(x) = \lfloor 10\log_x x! } \rfloor \]

Consider the inverse of \(f\), \(g(x) = f^{-1}(x) \). Each line of this 1000 line text file contains an integer \(i\), \(2 \leq i \leq 2 \times 10^9\). Find \( \sum g(i)\).

Details and Assumptions

  • \(\lfloor x \rfloor \) is the floor function. ie \(\lfloor 123456.789 \rfloor = 123456 \).

  • Here is an easier version of this problem.

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