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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 Niven's constant ： ウィキペディア英語版 Niven's constant In number theory, Niven's constant, named after Ivan Niven, is the largest exponent appearing in the prime factorization of any natural number ''n'' "on average". More precisely, if we define ''H''(1) = 1 and ''H''(''n'') = the largest exponent appearing in the unique prime factorization of a natural number ''n'' > 1, then Niven's constant is given by :$$ \lim_ \frac \sum_^n H(j) = 1+\sum_^\infty \left(1-\frac\right) = 1.705211\dots \, where ζ(''k'') is the value of the Riemann zeta function at the point ''k'' (Niven, 1969). In the same paper Niven also proved that :$$ \sum_^n h(j) = n + c\sqrt + o (\sqrt) \, where ''h''(1) = 1, ''h''(''n'') = the smallest exponent appearing in the unique prime factorization of each natural number ''n'' > 1, ''o'' is little o notation, and the constant ''c'' is given by :$$ c = \frac)}, \, and consequently that : $\backslash lim\_\; \backslash frac\backslash sum\_^n\; h(j)\; =\; 1.$ ==References== * * Steven R. Finch, ''Mathematical Constants'' (''Encyclopedia of Mathematics and its Applications''), Cambridge University Press, 2003 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「Niven's constant」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.