有关奇亏完全数的一些刻画

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (1): 158-167.

有关奇亏完全数的一些刻画

张四保^*1,2

1.喀什大学数学与统计学院, 新疆喀什 844000;
2.喀什大学现代数学及其应用研究中心, 新疆喀什 844000

收稿日期:2022-08-31 出版日期:2024-02-28 发布日期:2024-03-04
通讯作者: 张四保(1978-),男,江西峡江人,教授. Email:sibao98@sina.com
基金资助:
国家自然科学基金(12061039),新疆维吾尔自治区自然科学基金(2022D01A14)

Some characterizations on odd deficient-perfect numbers

ZHANG Si-bao^1,2

1. School of Mathematics and Statistics, Kashi University, Kashi 844000, China;
2. Research Center of Modern Mathematics and Its Application, Kashi University, Kashi 844000, China

Received:2022-08-31 Online:2024-02-28 Published:2024-03-04

摘要/Abstract

摘要： 为探讨具有5个相异素因数的奇亏完全数的存在性问题,通过奇亏完全数的定义以及初等方法研究了具有5个相异素因数的奇正整数n是否是奇亏完全数的问题,给出3类具有5个相异素因数的奇正整数n不是奇亏完全数的几个结论.

关键词: 亏完全数, 奇亏完全数, 存在性, 数论函数

Abstract: In order to study the existence of odd-deficient perfect numbers with five different prime factors, the problem whether odd positive integer n with five different prime factors satisfy the definition of the odd deficient perfect number is discussed by using the elementary method. Several conclusions indicating that there are three classes of odd positive integers n with five different prime factors are not odd deficient perfect number.

Key words: deficient-perfect number, odd deficient perfect number, existence, arithmetical function

中图分类号:

O156

张四保. 有关奇亏完全数的一些刻画[J]. 兰州理工大学学报, 2024, 50(1): 158-167.

ZHANG Si-bao. Some characterizations on odd deficient-perfect numbers[J]. Journal of Lanzhou University of Technology, 2024, 50(1): 158-167.

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