Is there a result in the spirit of Bertrand-Chebyshev which talks about the existence of prime powers between n and 2n (or 3n or something like that) for n large?



prime powers between n and 2n
It follows from the prime number theorem that for fixed $k$, provided $n$ is sufficiently large, there is a prime $p$ such that $p^k$ is between $n$ and $2n$. Does this answer your question? 


