文档介绍：DissertatiOR ofMaster 2012 Register Number:2009210589 Zhejiang Normal University Mean Value onSome Arithmetical Functions Department CQU殳g殳QfMath殳ma重i￡s￡h￥si￡墨and Specialty Direction Degree Advisor Name 里望!.01堡垒!iQ望垦坠gi望壁里!i望g Foundation Mathematics Science Master Date ofSubmission March 16, 2012 ,我们主要研究了三个问题中有关数论函数的均值. 首先,讨论的是罗马尼亚数论专家Florentin Smarandachc教授在《Only Problems,Not Solutions))一书中提出的问题6、7、(12),第礼项记为g(12),我们用初等方法分别研究了f(12)和g(12)的均值,并得到了一些有趣的渐近公式. 然后,’次可加补数复合和混合的数论函数,用初等及解析的方法对所得的复合函数和混合函数均值进行研究,得到了一些渐近公式. 最后,我们对关于正整数死的两个数论函数进行了研究,与研究?’次可加补数问题类似,先寻找能与关于正整数n的两个数论函数复合的数论函数,然后用初等及解析的方法对所得复合函数均值进行研究得到了一些渐近公式. 关键词:可构造序列;数字之和;r次可加补数;7'次幂因子;无7’次幂因子;欧拉函数o,均值;渐近公式 MEAN VALUE ON SOME ARITHMETICAL FUNCTlONS ABSTRACT Arithmetical function is areal—valued plex-valued function defined on the setofpositive research on themeal3value ofarithmetical func— tions is an important thisthesis,we investigate tothemean value on arithmetical functions inthree problems. First,we discuss the 6th,7th and 8thquestions about structured sequences inthe book of((Only Problems,Not Solutions))that written by American- Romanian number theorist Florentin f(n)is the sum ofeach digit ofthe n-th item inthissequence,and letg(n)is the n- use elementary methods toresearch themean valucof/(n)and夕(死),and get some interestingasymptotic formulas. Then,we research the r-thpower Look forsome functions which can pounded ormixed with ther-thpower additive corn— plement,and use elementary or analyzing methods toresearch themean value Oil posite and blended functions toget some asymptotic formulas. Finally,we research two arithmetical functions about positive integer similar,we use elementary and analyzing methods toresearch themean value of posite functions togetsomc asymptotic formulas. KEY WORD S: structuredsequence;digital sum;