SPOOF ODD PERFECT NUMBERS

被引：4
作者：
Dittmer, Samuel J. [1 ]
机构：
[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA
来源：
MATHEMATICS OF COMPUTATION | 2014年 / 83卷 / 289期
关键词：
D O I：
10.1090/S0025-5718-2013-02793-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In 1638, Descartes showed that 3(2) . 7(2) . 11(2) . 13(2) . 22021(1) would be an odd perfect number if 22021 were prime. We give a formal definition for such "spoof" odd perfect numbers, and construct an algorithm to find all such integers with a given number of distinct quasi-prime factors. We show that Descartes' example is the only spoof with less than seven such factors.
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收藏
页码：2575 / 2582
页数：8
相关论文
共 7 条
[1]  
Cook R. J., 1996, CRM P LECT NOTES, V19, P67
[2]  
Dickson L. E., 2005, History of the Theory of Numbers, Vol. 1: Divisibility and Primality, V1
[3]  
Euler L., 1849, COMMENTATIONES ARITH, V2, P514
[4]   ODD PERFECT NUMBERS [J].
HEATHBROWN, DR .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1994, 115 :191-196
[5]  
Nielsen P. P., 2003, INTEGERS, V3, pA14
[6]   Odd perfect numbers have at least nine distinct prime factors [J].
Nielsen, Pace P. .
MATHEMATICS OF COMPUTATION, 2007, 76 (260) :2109-2126
[7]  
Nielsen Pace P., 2013, PREPRINT
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