关于几个Smarandache函数性质的研究

发布时间：2018-03-12 15:26

  本文选题：Smarandache　切入点：LCM函数　出处：《延安大学》2017年硕士论文　论文类型：学位论文

【摘要】：摘要:Smarandache函数是数论研究的重要内容之一,随着人们对它的深入探索和研究,目前已经出现了很多类函数方程和研究方法.本文在阅读大量与Smarandache问题相关的书籍和文献的基础上,主要利用初等方法和解析方法对几个Smarandache函数问题进行研究,具体内容如下:首先,研究了两个包含Smarandache LCM函数方程S(SL(n)=(?)e(n)和Z(SL(n))=()?e(n)在e = 1,2时的可解性问题,给出了方程的所有正整数解;其次,研究了关于Smarandache LCM函数在简单数序列上的均值性质,给出并证明了(?)和(?)的两个渐近公式.并对SmarandacheLCM函数SL(n)与最大素因子函数之差的β次方的值分布问题和一个Smarandache可乘函数与最大素因子函数的β次混合均值问题进行了探讨研究,最终给出并证明了(?)(SL(n)-P(n))β和(?)(f(Pd(n))—1/2d(n)P(n))β的渐近公式;最后,研究了 Smarandache LCM函数SL(n)在特殊序列2p±1上的下界估计问题,给出并证明SL(2p±1)≥10p+1,其中素数p≥17.
[Abstract]:The function of: Smarandache is one of the important contents in the study of number theory. With the deep exploration and research on it, there have been many kinds of functional equations and research methods. This paper mainly studies several Smarandache function problems by using elementary method and analytic method. The main contents are as follows: firstly, two Smarandache LCM function equations are studied. A) and a Zang SLN (a) and a sling (a) and a little bit (a)? In this paper, we give all positive integer solutions of the equation at e = 1, 2:00. Secondly, we study the mean value properties of Smarandache LCM functions on simple number sequences, and give and prove the results. ) and Ko? And the problem of the value distribution of the difference between the SmarandacheLCM function and the maximal prime factor function and the 尾 th mixed mean value problem of a Smarandache multiplicative function and the maximal prime factor function are studied. Finally, the author gives and proves the problem of the 尾 th order mixed mean value of the Smarandache multiplicative function and the maximal prime factor function. The 尾 and P??? Finally, the lower bound estimation problem of Smarandache LCM function on a special sequence 2p 卤1 is studied, and it is proved that SL(2p 卤1) 鈮，

本文编号：1602160