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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 Unusual number ： ウィキペディア英語版 Unusual number In number theory, an unusual number is a natural number ''n'' whose largest prime factor is strictly greater than $\backslash sqrt$ . All prime numbers are unusual. A ''k''-smooth number has all its prime factors less than or equal to ''k'', therefore, an unusual number is non-$\backslash sqrt$-smooth. The first few unusual numbers are 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67.... The first few non-prime unusual numbers are 6, 10, 14, 15, 20, 21, 22, 26, 28, 33, 34, 35, 38, 39, 42, 44, 46, 51, 52, 55, 57, 58, 62, 65, 66, 68, 69, 74, 76, 77, 78, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 99, 102.... For any prime p, its multiples less than p² are unusual, that is p, ... (p-1)p, which have a density 1/p in the interval (p,p²). If we denote the number of unusual numbers less than or equal to ''n'' by ''u''(''n'') then ''u''(''n'') behaves as follows: Richard Schroeppel stated in 1972 that the asymptotic probability that a randomly chosen number is unusual is ln(2). In other words: :$\backslash lim\_\; \backslash frac\; =\; \backslash ln(2)\; =\; 0.693147\; \backslash dots\backslash ,\; .$ == External links == * 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「Unusual number」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.