|
In number theory, a natural number is called almost prime if there exists an absolute constant ''K'' such that the number has at most ''K'' prime factors. An almost prime ''n'' is denoted by ''Pr'' if and only if the number of prime factors of ''n'', counted according to multiplicity, is at most ''r''. A natural number is called ''k''-almost prime if it has exactly ''k'' prime factors, counted with multiplicity. 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'': : 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 ''P''''k''. The smallest ''k''-almost prime is 2''k''. The first few ''k''-almost primes are: : The number π''k''(''n'') of positive integers less than or equal to ''n'' with at most ''k'' prime divisors (not necessarily distinct) is asymptotic to: : a result of Landau. See also the Hardy–Ramanujan theorem. ==References== 〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「almost prime」の詳細全文を読む スポンサード リンク
|