Consider the Mersenne number; $M_p=2^p−1$. Let $M_p=a_pb^2_p$ where $a_p$ is positive, squarefree, and $p$ is prime.

A chinese paper written by Le Maohua "“On Mersenne Numbers”" states that the squarefree part of $M_p$ is greater than $(πp/log p)^2$.

As the paper is in chinese I could not figure out how the result is obtained. Can someone help me out?

Thank you...

Consider the Mersenne number; $M_p=2^p−1$. Let $M_p=a_pb^2_p$ where $a_p$ is positive, squarefree, and $p$ is prime.

A chinese paper written by Le Maohua "“On Mersenne Numbers”" states that the squarefree part of $M_p$ is greater than $(πp/\log p)^2$.

As the paper is in chinese I could not figure out how the result is obtained. Can someone help me out?

Thank you...