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数学进展 - 2016, Vol. 45(2): 190-194
研究论文
关于k重unitary完全数
On Unitary \mbox{\boldmath $k$}-perfect Numbers

汤敏1,杨全会2
TANG Min1, YANG Quanhui2

1.安徽师范大学数学计算机科学学院, 芜湖, 安徽, 241003;
2.南京信息工程大学数学与统计学院, 南京, 江苏, 210044
1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui, 241003, P. R. China;
2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, 210044,P. R. China

收稿日期: 2014-09-01
2016, Vol. 45(2): 190-194
DOI: 10.11845/sxjz.2014133b


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摘要 给定正整数$N$, 如果$d\mid N$且$(d,\frac{N}{d})=1$, 则称$d$为$N$的unitary因子. 设$k\geq 2$为整数, $\sigma^\ast(N)$ 表示$N$ 的所有unitary因子的和. 若$\sigma^\ast(N)=kN$, 则称$N$为$k$重unitary完全数. 本文给出了$k$重unitary完全数的一些性质.
Abstract:For a positive integer $N$, we call $d$ a unitary divisor of $N$ if $d\mid N$ and $(d,\frac{N}{d})=1$.Let $k\geq 2$ be an integer, and let $\sigma^\ast(N)$ denote the sum of the unitary divisors of $N$. We call $N$ a unitary $k$-perfect number if $\sigma^\ast(N)=kN$. In this paper, we give some necessary properties of them.
PACS:  O156.1  
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[1] 刘鑫媛,方金辉. 关于加法补集的一个注记[J]. 数学进展, 2016, 45(4): 533-536.
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