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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 Unitary divisor ： ウィキペディア英語版 Unitary divisor In mathematics, a natural number ''a'' is a unitary divisor of a number ''b'' if ''a'' is a divisor of ''b'' and if ''a'' and $\backslash frac$ are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and $\backslash frac=12$ have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and $\backslash frac=10$ have a common factor other than 1, namely 2. 1 is a unitary divisor of every natural number. Equivalently, a given divisor ''a'' of ''b'' is a unitary divisor if and only if every prime factor of ''a'' has the same multiplicity in ''a'' as it has in ''b''. The sum of unitary divisors function is denoted by the lowercase Greek letter sigma thus: σ *(''n''). The sum of the ''k''-th powers of the unitary divisors is denoted by σ *k(''n''): :$\backslash sigma\_k^$ *(n) = \sum_ \!\! d^k. If the proper unitary divisors of a given number add up to that number, then that number is called a unitary perfect number. ==Properties== The number of unitary divisors of a number ''n'' is 2''k'', where ''k'' is the number of distinct prime factors of ''n''. The sum of the unitary divisors of ''n'' is odd if ''n'' is a power of 2 (including 1), and even otherwise. Both the count and the sum of the unitary divisors of ''n'' are multiplicative functions of ''n'' that are not completely multiplicative. The Dirichlet generating function is :$\backslash frac\; =\; \backslash sum\_\backslash frac.$ Every divisor of ''n'' is unitary if and only if ''n'' is square-free. 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「Unitary divisor」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.