Solutions of the congruence 1+2f (n) + . . . + nf (n) ≡ 0 (mod n)

被引：4
|
作者：
Maria Grau, Jose [1 ]
Moree, Pieter [2 ]
Oller-Marcen, Antonio M. [3 ]
机构：
[1] Univ Oviedo, Dept Matemat, Avda Calvo Sotelo S-N, Oviedo 33007, Spain
[2] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany
[3] Ctr Univ Def Zaragoza, Ctra Huesca S-N, Zaragoza 50090, Spain
来源：
MATHEMATISCHE NACHRICHTEN | 2016年 / 289卷 / 07期
关键词：
Power sums; congruence; divisibility; asymptotic density; Giuga numbers;
D O I：
10.1002/mana.201500057
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we characterize, in terms of the prime divisors of n, the pairs (k, n) for which n divides Sigma(n)(j=1) j(k). As an application, we derive some results on the sets M-f := {n >= 1 : f (n) > 1 and Sigma(n)(j=1) j(f (n)) equivalent to 0 (mod n)} for some choices of f. C (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
引用
收藏
页码：820 / 830
页数：11
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