Almost prime

In number theory, a natural number is called k-almost prime if it has k prime factors.

[1][2][3] More formally, a number n is k-almost prime if and only if Ω(n) = k, where Ω(n) is the total number of primes in the prime factorization of n (can be also seen as the sum of all the primes' exponents): A natural number is thus prime if and only if it is 1-almost prime, and semiprime if and only if it is 2-almost prime.

The set of k-almost primes is usually denoted by Pk.

The smallest k-almost prime is 2k.

The first few k-almost primes are: The number πk(n) of positive integers less than or equal to n with exactly k prime divisors (not necessarily distinct) is asymptotic to:[4] a result of Landau.