# 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 $$i$$, $$2 \leq i \leq 2 \times 10^{10}$$. 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.

×