18693.關(guān)于smarandache函數(shù)s(n)的性質(zhì)研究

1、關(guān)于smarandache函數(shù)S(億)的性質(zhì)研究ResearchesonPropertiesoftheSmarandacheFunctionS(佗)作者：王麗麗Author：!豎壘里g墜i!i指導(dǎo)教師：朱偉義專業(yè)：基礎(chǔ)數(shù)學(xué)Supervisor：圣墜墜!豎iYiMajor：BasicMathematics學(xué)位：堡堂塹～Degree：叢箜!竺Q!量里i塑里里授予單位：浙江師范大學(xué)Institute：圣塾gi壘翌g盟Q!坐壘!墮望i!皇!曼i

2、!∑May，2015AbstractForanypositiveinteger佗，thefamousSmarandachefunctionS(訖)isdefinedasthesmallestpositiveintegermandnm!，thatiss(仡)=minm：nm!)Letnbeanypositiveinteger，iftheproductofallproperfactorsof咒islessthanorequalto乃，the

3、nnissaidasimplenumberTherearefivechaptersinthisthesisInChapter1，thebackgroundandthesignificanceofresearch，includetheresearchprogressabouttheSmarandachefunctionS(n)，thesequenceofsimplenumbersandprimitivenumberofpowerPThem

4、ainresultsandthecontentorganizationofthisthesisarealsogivenInChapter2，preliminariesrelatedtotheresearch，includeseveralclassicalarith—meticfunctionsandthefamousSmarandachefunction^S(n)，Abelidentity，andEulersummationformul

5、aInChapter3，weconsiderthemeanvaluepropertiesoffunctionS(佗)aboutthesequenceofsimplenumbersbyusingelementarymethod，andtwointerestingasymptoticformulasaregivenInChapter4，weinvestigatethemeanvaluepropertiesofarithmeticfuncti

6、onsthatcontainfunctions(n)aboutthesequenceofsimplenumbers，includeseveralclassicalarithmeticfunctionsandotherfamousSmarandachefunctionInChapter5，weconsidersomepropertiesofprimitivenumberofpowerPFromtheknownrelationshipbet

7、weenfunction品(n2)and品(n)，furtherpromotetotherelation—shipbetweenfunction昂(n2)and昂(n)，thecorrespondencebetweenthevaluesof昂(n)andthenumberofitemsisalsostudiedKeywords：SmarandachefunctionS(n)；simplenumber；meanvalueproperty；