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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 Pillai's arithmetical function ： ウィキペディア英語版 Pillai's arithmetical function In number theory, the gcd-sum function, also called Pillai's arithmetical function,〔 is defined for every $n$ by :$P(n)=\backslash sum\_^n\backslash gcd(k,n)$ or equivalently〔 :$P(n)\; =\; \backslash sum\_\; d\; \backslash varphi(n/d)$ where $d$ is a divisor of $n$ and $\backslash varphi$ is Euler's totient function. it also can be written as〔(http://math.stackexchange.com/questions/135351/sum-of-gcdk-n )〕 :$P(n)\; =\; \backslash sum\_\; d\; \backslash sigma(d)\; \backslash mu(n/d)$ where, $\backslash sigma$ is the Divisor function, and $\backslash mu$ is the Möbius function. This multiplicative arithmetical function was introduced by the Indian mathematician Subbayya Sivasankaranarayana Pillai in 1933. ==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「Pillai's arithmetical function」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.