In number theory, a natural number is called k-almost prime if it has k prime factors. 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: a result of Landau. See also the Hardy–Ramanujan theorem.

Properties

k1 -almost prime and a k2 -almost prime is a (k1 + k2) -almost prime. n > k .