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Scientia Magna : An International Journal : Volume 1, No. 1, 2005

By Yanni, Liu

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Book Id: WPLBN0002828560
Format Type: PDF (eBook)
File Size: 1.50 mb
Reproduction Date: 8/7/2013

Title: Scientia Magna : An International Journal : Volume 1, No. 1, 2005  
Author: Yanni, Liu
Volume: Volume 1, No. 1, 2005
Language: English
Subject: Non Fiction, Education, Algebra
Collection: Authors Community
Subcollection: Mathematics
Publication Date:
Publisher: World Public Library
Member Page: Florentin Smarandache

The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache function, and give an interesting asymptotic formula.

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies.

x1. Introduction In reference [1], the Smarandache Sum of Composites Between Factors function SCBF(n) is defined as: The sum of composite numbers between the smallest prime factor of n and the largest prime factor of n. For example, SCBF(14)=10, since 2£7 = 14 and the sum of the composites between 2 and 7 is: 4 + 6 = 10. In reference [2]: A number n is called simple number if the product of its proper divisors is less than or equal to n. Let A denotes set of all simple numbers. That is, A = f2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 13; 14; 15; 17; 19; 21.

Table of Contents
On the Smarandache function and square complements 1 Zhang Wenpeng , Xu Zhefeng On the integer part of the k -th root of a positive integer 5 Zhang Tianping , Ma Yuankui Smarandache “Chopped” NN and N + 1N¡1 9 Jason Earls The 57 -th Smarandache’s problem II 13 Liu Huaning , Gao Jing Perfect Powers in Smarandache n - Expressions 15 Muneer Jebreel Karama On the m -th power residue of n 25 Li Junzhuang and Zhao Jian Generalization of the divisor products and proper divisor products sequences 29 Liang Fangchi The science of lucky sciences 33 Jon Perry Smarandache Sequence of Unhappy Numbers 37 Muneer Jebreel Karama On m -th power free part of an integer 39 Zhao Xiaopeng and Ren Zhibin On two new arithmetic functions and the k -power complement number sequences 43 Xu Zhefeng Smarandache Replicating Digital Function Numbers 49 Jason Earls On the m -power residues numbers sequence 53 Ma Yuankui , Zhang Tianping Smarandache Reverse Power Summation Numbers 57 Jason Earls Some Smarandache Identities 59 Muneer Jebreel Karama On the integer part of a positive integer’s k -th root 61 Yang Hai , Fu Ruiqin Smarandache Friendly Cube Numbers 67 Muneer Jebreel Karama Some Expressions of the Smarandache Prime Function 71 Sebastian Martin Ruiz An Improved Algorithm for Calculating the Sum-of-Factorials Function 75 Jon Perry On the Smarandche function and its hybrid mean value 79 Yao Weili On the 83 -th Problem of F. Smarandache 83 Gao Nan On Smarandache triple factorial function 89 You Qiying On k -factorials and Smarandacheials 93 Jon Perry A note on Exponential Divisors and Related Arithmetic Functions 97 J¶ozsef S¶andor Smarandache multiplicative function 103 Liu Yanni , Gao Peng Two formulas for Smarandache LCM ratio sequences 109 Wang Ting The 97 -th problem of F.Smarandache 115 Yi Yuan On Two Subsets of Generalized Smarandache Palindromes 119 Jason Earls The Smarandache factorial sequence 123 Zhang Xiaobeng The Smarandache multiplicative function 125 Ma Jinping On Consecutive Values of the Smarandache Function 129 Jason Earls On the 82-th Smarandache’s Problem 131 Fu Ruiqin, Yang Hai On a New Class of Smarandache Prime Numbers 135 Jason Earls On the odd sieve sequence 137 Yao Weili On the k-power part residue function 141 Yang Hai, Fu Ruiqin Mean value of the additive analogue of Smarandache function 145 Yi Yuan and Zhang Wenpeng Hybrid mean value on some Smarandache-type multiplicative functions and the Mangoldt function 149 Liu Huaning, Gao Jing On a number set related to the k-free numbers 153 Li Congwei Smarandache Pseudo– Happy numbers 157 Anant W. Vyawahare A number theoretic function and its mean value 163 Ren Ganglian A new function and its mean value 167 Ding Liping On the m-power complement numbers 171 Zhang Xiaobeng On the primitive numbers of power p and its asymptotic property 175 Yi Yuan Mean value of the additive analogue of Smarandache function 179 Zhu Minhui On the generalization of the floor of the square root sequence 183 Yao Weili Mean value of a new arithmetic function 187 Liu Yanni, Gao Peng On the number of numbers with a given digit sum 191 Jon Perry On the mean value of the Smarandache double factorial function 197 Zhu Minhui On the m -power free part of an integer 203 Liu Yanni , Gao Peng On the mean value of the SCBF function 207 Zhang Xiaobeng


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