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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Almost prime ： ウィキペディア英語版 Almost prime 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'': :$\backslash Omega(n)\; :=\; \backslash sum\; a\_i\; \backslash qquad\backslash mbox\backslash qquad\; n\; =\; \backslash prod\; p\_i^.$ 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: : $\backslash pi\_k(n)\; \backslash sim\; \backslash left(\; \backslash frac\; \backslash right)\; \backslash frac,$ 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.