本文選題：Smarandache　切入點：LCM函數　出處：《延安大學》2017年碩士論文　論文類型：學位論文

【摘要】：摘要:Smarandache函數是數論研究的重要內容之一,隨著人們對它的深入探索和研究,目前已經出現了很多類函數方程和研究方法.本文在閱讀大量與Smarandache問題相關的書籍和文獻的基礎上,主要利用初等方法和解析方法對幾個Smarandache函數問題進行研究,具體內容如下:首先,研究了兩個包含Smarandache LCM函數方程S(SL(n)=(?)e(n)和Z(SL(n))=()?e(n)在e = 1,2時的可解性問題,給出了方程的所有正整數解;其次,研究了關于Smarandache LCM函數在簡單數序列上的均值性質,給出并證明了(?)和(?)的兩個漸近公式.并對SmarandacheLCM函數SL(n)與最大素因子函數之差的β次方的值分布問題和一個Smarandache可乘函數與最大素因子函數的β次混合均值問題進行了探討研究,最終給出并證明了(?)(SL(n)-P(n))β和(?)(f(Pd(n))—1/2d(n)P(n))β的漸近公式;最后,研究了 Smarandache LCM函數SL(n)在特殊序列2p±1上的下界估計問題,給出并證明SL(2p±1)≥10p+1,其中素數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 鹵1 is studied, and it is proved that SL(2p 鹵1) 鈮，

本文編號：1602160