  The author \cite{4} proved that, for every set $S$ of positive integers
containing 1 (finite or infinite) there exists the density $h=h(E(S))$ of the
set $E(S)$ of numbers whose prime factorizations contain exponents only from
$S,$ and gave an explicit formula for $h(E(S)).$ In this paper we give an
equivalent polynomial formula for $\log h(E(S))$ which allows to get a fast
calculation of $h(E(S)).$
