We compare and contrast three methods for estimating the number of integers in an interval of length x which have fewer than k distinct prime factors less than z, with special attention to the case k = 2. An iterative method based on the case k = 1 is simplest. If z is sufficiently small compared to x one may use a kind of Brun sieve. Selberg's sieve method gives a good estimate for k = 2 but leads into technical difficulties as k increases. 1978.
