Sequence m(k) with $\frac{m(k)}{3\cdot k\cdot log(k)}>0$ for $k\rightarrow\infty$

Question

I'm looking for a sequence m(k) which fullfills the condition $\frac{m(k)}{3\cdot k\cdot log(k)}>0$ for $k\rightarrow\infty$. log(k) means the natural logarithm and m,k are positive integers. Thanks for help!

Answer 1

Given $\varepsilon>0$, it is enough to set $$ m(k)=k^{1+\varepsilon}. $$

For a more interesting solution, you could choose $$ m(k)=4p_k, $$ where $p_k$ is the $k$-th prime :)