ON NEAR-PERFECT NUMBERS

被引：5

作者：

Tang, Min ^{[1
]}

Ma, Xiaoyan ^{[1
]}

Feng, Min ^{[1
]}

机构：

[1] Anhui Normal Univ, Sch Math & Comp Sci, Wuhan 241003, Peoples R China

来源：

COLLOQUIUM MATHEMATICUM | 2016年 / 144卷 / 02期

关键词：

near-perfect number; redundant divisor; quasiperfect number;

D O I：

10.4064/cm6588-10-2015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a positive integer n, let sigma(n) denote the sum of the positive divisors of n. We call n a near-perfect number if sigma(n) = 2n + d where d is a proper divisor of n. We show that the only odd near-perfect number with four distinct prime divisors is 3(4) . 7(2) . 11(2) . 19(2).

引用

页码：157 / 188

页数：32

共 50 条

[1] On perfect and near-perfect numbers
Pollack, Paul
Shevelev, Vladimir
JOURNAL OF NUMBER THEORY, 2012, 132 (12) : 3037 - 3046
[2] On near-perfect numbers
Cohen, Peter
Cordwell, Katherine
Epstein, Alyssa
Kwan, Chung-Hang
Lott, Adam
Miller, Steven J.
ACTA ARITHMETICA, 2020, 194 (04) : 341 - 366
[3] ON NEAR-PERFECT AND DEFICIENT-PERFECT NUMBERS
Tang, Min
Ren, Xiao-Zhi
Li, Meng
COLLOQUIUM MATHEMATICUM, 2013, 133 (02) : 221 - 226
[4] ON NEAR-PERFECT NUMBERS OF SPECIAL FORMS
Hasanalizade, Elchin
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2023, 108 (03) : 366 - 372
[5] A CLASS OF NEW NEAR-PERFECT NUMBERS
Li, Yanbin
Liao, Qunying
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2015, 52 (04) : 751 - 763
[6] ON NEAR-PERFECT NUMBERS WITH TWO DISTINCT PRIME FACTORS
Ren, Xiao-Zhi
Chen, Yong-Gao
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2013, 88 (03) : 520 - 524
[7] Near-perfect model
Miller, Richard
NEW SCIENTIST, 2007, 196 (2630) : 24 - 24
[8] A 'Near-Perfect Gift'
Kinder, RM
SOUTHERN HUMANITIES REVIEW, 1999, 33 (01): : 64 - 77
[9] Near-perfect pitch
Ackman, D
FORBES, 2004, 173 (13): : 184 - 184
[10] Near-perfect 'black'
Ball, Philip
NATURE, 2008, 453 (7197) : 834 - 834

← 1 2 3 4 5 →