Multiperfect numbers on lines of the Pascal triangle

作     者：Luca, Florian Luis Varona, Juan 

作者机构：Univ La Rioja Dpto Matemat & Computac Logrono 26004 Spain Univ Nacl Autonoma Mexico Inst Matemat Morelia 58089 Michoacan Mexico 

出 版 物：《JOURNAL OF NUMBER THEORY》 (数论杂志)

年 卷 期：2009年第129卷第5期

页      面：1136-1148页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：DGI [MTM2006-13000-C03-03] SEP-CONACyT 79685 

主　　题：Multiperfect Multiply perfect Perfect Sum of divisors Pascal triangle Binomial coefficients Catalan numbers 

摘      要：A number n is said to be multiperfect (or multiply perfect) if n divides its sum of divisors sigma(n). In this paper, we study the multiperfect numbers on straight lines through the Pascal triangle. Except for the lines parallel to the edges, we show that all other lines through the Pascal triangle contain at most finitely many multiperfect numbers. We also study the distribution of the numbers sigma(n)/n whenever the positive integer n ranges through the binomial coefficients on a fixed line through the Pascal triangle. (C) 2008 Elsevier Inc. All rights reserved.