Question 13
Find the smallest positive integer $k$ such that $\displaystyle\frac1{\log_{2^k}(2019!)}+\frac1{\log_{3^k}(2019!)}+\frac1{\log_{4^k}(2019!)}+\cdots+\frac1{\log_{2019^k}(2019!)}\gt \sqrt{2019}$.
Enter the exact number only; fractions are allowed.
Enter the exact number only; fractions are allowed.