  In this work, we obtain some new lower bounds for the number $\mathcal
N_B(x)$ of Nov\'ak 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 Nov\'ak number and give description for
the prime factors of Nov\'ak numbers $N$, such that $2N$ is a
Nov\'ak-Carmichael number.
