  A semiprime is a natural number which can be written as the product of two
primes. The asymptotic behaviour of the function $\pi_2(x)$, the number of
semiprimes less than or equal to $x$, is studied. Using a combinatorial
argument, asymptotic series of $\pi_2(x)$ is determined, with all the terms
explicitly given. An algorithm for the calculation of the constants involved in
the asymptotic series is presented and the constants are computed to 20
significant digits. The errors of the partial sums of the asymptotic series are
investigated. A generalization of this approach to products of $k$ primes, for
$k\geq 3$, is also proposed.
