Address:
School of Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein 2000, Johannesburg, South Africa, and Research Group Algebraic Structures and Applications, King Abdulaziz University, Jeddah, Saudi Arabia, and Max Planck Institute for Mathematics, Vivatsgasse 7, Bonn 53111, Germany, and Department of Mathematics, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
School of Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein 2000, Johannesburg, South Africa
E-mail:
florian.luca@wits.ac.za
747011@students.wits.ac.za
Abstract: In this note, we show that the counting function of the number of composite positive integers $n\le x$ such that $\beta (n)=\sum _{p\mid n} p$ is a prime is of order of magnitude at least $x/(\log x)^3$ and at most $x/ \log x$.
AMSclassification: primary 11N25; secondary 11N36.
Keywords: primes, applications of sieve methods.
DOI: 10.5817/AM2020-1-49