On The Smarandache Function And The Divisor Product Sequences
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On The Smarandache Function And The Divisor Product Sequences
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Author : Mingdong Xiao
language : en
Publisher: Infinite Study
Release Date :
On The Smarandache Function And The Divisor Product Sequences written by Mingdong Xiao and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Let n be any positive integer, Pd(n) denotes the product of all positive divisors of n. The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of a new arithmetical function S (Pd(n)), and give an interesting asymptotic formula for it.
Smarandache Function Journal Vol 14 2004
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Author : Sabin Tabirca
language : en
Publisher: Infinite Study
Release Date :
Smarandache Function Journal Vol 14 2004 written by Sabin Tabirca and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Research On Smarandache Problems In Number Theory Collected Papers Vol I
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Author : Wenpeng Zhang
language : en
Publisher: Infinite Study
Release Date : 2005-01-01
Research On Smarandache Problems In Number Theory Collected Papers Vol I written by Wenpeng Zhang and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
Number theory is an ancient subject, but we still cannot answer many simplest and most natural questions about the integers. Some old problems have been solved, but more arise. All the research for these ancient or new problems implicated and are still promoting the development of number theory and mathematics.American-Romanian number theorist Florentin Smarandache introduced hundreds of interest sequences and arithmetical functions, and presented many problems and conjectures in his life. In 1991, he published a book named Only problems, Not solutions!. He presented 105 unsolved arithmetical problems and conjectures about these functions and sequences in it. Already many researchers studied these sequences and functions from his book, and obtained important results.This book, Research on Smarandache Problems in Number Theory (Collected papers), contains 41 research papers involving the Smarandache sequences, functions, or problems and conjectures on them.All these papers are original. Some of them treat the mean value or hybrid mean value of Smarandache type functions, like the famous Smarandache function, Smarandache ceil function, or Smarandache primitive function. Others treat the mean value of some famous number theoretic functions acting on the Smarandache sequences, like k-th root sequence, k-th complement sequence, or factorial part sequence, etc. There are papers that study the convergent property of some infinite series involving the Smarandache type sequences. Some of these sequences have been first investigated too. In addition, new sequences as additive complement sequences are first studied in several papers of this book.Most authors of these papers are my students. After this chance, I hope they will be more interested in the mysterious integer and number theory!More future papers by my students will focus on the Smarandache notions, such as sequences, functions, constants, numbers, continued fractions, infinite products, series, etc. in number theory!List of the Contributors:Zhang Wenpeng, Xu Zhefeng, Zhang Xiaobeng, Zhu Minhui, Gao Nan, Guo Jinbao, He Yanfeng, Yang Mingshun, Li Chao, Gao Jing, Yi Yuan, Wang Xiaoying, Lv Chuan, Yao Weili, Gou Su, He Xiaolin, Li Hailong, Liu Duansen, Li Junzhuang, Liu Huaning, Zhang Tianping, Ding Liping, Li Jie, Lou Yuanbing, Zhao Xiqing, Zhao Xiaopeng, Yang Cundian, Liang Fangchi
Smarandache Notions Journal Vol 13
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Author : Jack Allen
language : en
Publisher: Infinite Study
Release Date : 2002-12-01
Smarandache Notions Journal Vol 13 written by Jack Allen and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-01 with Mathematics categories.
Scientia Magna Vol 5 No 2 2009
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Author : Zhang Wenpeng
language : en
Publisher: Infinite Study
Release Date : 2009
Scientia Magna Vol 5 No 2 2009 written by Zhang Wenpeng and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
A collection of articles on smarandache notions in number theory.
Smarandache Function Journal Vol 10 1999
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Author : V. Seleacu
language : en
Publisher: Infinite Study
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Smarandache Function Journal Vol 10 1999 written by V. Seleacu and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Generalized Partitions And New Ideas On Number Theory And Smarandache Sequences
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Author : Amarnath Murthy
language : en
Publisher: Infinite Study
Release Date : 2005-01-01
Generalized Partitions And New Ideas On Number Theory And Smarandache Sequences written by Amarnath Murthy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
Florentin Smarandache is an incredible source of ideas, only some of which are mathematical in nature. Amarnath Murthy has published a large number of papers in the broad area of Smarandache Notions, which are math problems whose origin can be traced to Smarandache. This book is an edited version of many of those papers, most of which appeared in Smarandache Notions Journal, and more information about SNJ is available at http://www.gallup.unm.edu/~smarandache/ . The topics covered are very broad, although there are two main themes under which most of the material can be classified. A Smarandache Partition Function is an operation where a set or number is split into pieces and together they make up the original object. For example, a Smarandache Repeatable Reciprocal partition of unity is a set of natural numbers where the sum of the reciprocals is one. The first chapter of the book deals with various types of partitions and their properties and partitions also appear in some of the later sections.The second main theme is a set of sequences defined using various properties. For example, the Smarandache n2n sequence is formed by concatenating a natural number and its double in that order. Once a sequence is defined, then some properties of the sequence are examined. A common exploration is to ask how many primes are in the sequence or a slight modification of the sequence. The final chapter is a collection of problems that did not seem to be a precise fit in either of the previous two categories. For example, for any number d, is it possible to find a perfect square that has digit sum d? While many results are proven, a large number of problems are left open, leaving a great deal of room for further exploration.
Smarandache Notions Vol 14
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2004-01-01
Smarandache Notions Vol 14 written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Number theory categories.
Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that there is no speed barrier in the universe, quantum paradoxes, etc. have been selected for this volume. Contributors are from Australia, China, England, Germany, India, Ireland, Israel, Italy, Japan, Malaysia, Morocco, Portugal, Romania, Spain, USA. Most of the papers are in English, a few of them are in Spanish, Portuguese, or German.
Scientia Magna Vol 5 No 3 2009
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Author : Zhang Wenpeng
language : en
Publisher: Infinite Study
Release Date :
Scientia Magna Vol 5 No 3 2009 written by Zhang Wenpeng and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Papers on Smarandache magic square, Smarandache friendly numbers, some another remarks on the generalization of Bernoulli and Euler numbers, an integral identity involving the Hermite polynomials, vinegar identifiation by ultraviolet spectrum technology and pattern recognition method, pairwise semi compact and pairwise semi lindeloff spaces, and other topics. Contributors: C. Prabpayak, U. Leerawat, S. M. Khairnar, S. Balasubramanian, B. Amudhambigai, A. H. Majeed, A. D. Hamdi, H. Jolany, M. R. Darafsheh, and others.
Scientia Magna International Book Series Vol 13 No 1
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Author : Huaning Liu
language : en
Publisher: Infinite Study
Release Date :
Scientia Magna International Book Series Vol 13 No 1 written by Huaning Liu and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Scientia Magna international book series are published in one or two volumes per year with more than 100 pages and over 1,000 copies.