On Novák numbers

Abstract

In this work, we obtain some new lower bounds for the number ${\mathcal{N}}_B(x)$ of Novák numbers less than or equal to $x$. We also prove, conditionally on Generalized Riemann Hypothesis, the upper estimates for the number of primes dividing at least one Novák number and give description for the prime factors of Novák numbers $N$, such that $2N$ is a Novák-Carmichael number.

12 pages; typos corrected