Normal numbers and the middle prime factor of an integer
Volume 135 / 2014
Colloquium Mathematicum 135 (2014), 69-77
MSC: Primary 11K16; Secondary 11N37.
DOI: 10.4064/cm135-1-5
Abstract
Let $p_m(n)$ stand for the middle prime factor of the integer $n\ge 2$. We first establish that the size of $\log p_m(n)$ is close to $\sqrt {\log n}$ for almost all $n$. We then show how one can use the successive values of $p_m(n)$ to generate a normal number in any given base $D\ge 2$. Finally, we study the behavior of exponential sums involving the middle prime factor function.
