  In 2005, E. Noel and G. Panos constructed a formula to count the number of
semiprimes less than a given value $x$. In 2006, this formula was rediscovered
independently by R.G. Wilson V. However, each citation of this result was
simply through personal communication, and a formal proof has not been written
down anywhere in the literature. In this article, we generalize their formula
to the case of $k$-almost primes and square-free $k$-almost primes.
