  An integer $n$ is said to be ternary if it is composed of three distinct odd
primes. In this paper, we asymptotically count the number of ternary integers
$n \leq x$ with the constituent primes satisfying various constraints. We apply
our results to the study of the simplest class of (inverse) cyclotomic
polynomials that can have coefficients that are greater than 1 in absolute
value, namely to the $n^{th}$ (inverse) cyclotomic polynomials with ternary
$n$. We show, for example, that the corrected Sister Beiter conjecture is true
for a fraction $\ge 0.925$ of ternary integers.
