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

By Yanni, Liu

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

Description
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.

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

Excerpt
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