ScholarLens Back to search
2003•Unpublished venueRequires access

POSITIVE INTEGERS n SUCH THAT n|a σ(n) − 1

Florian Luca

Open publisher page 0 citations

Abstract

Abstract. For a positive integer n let σ(n) be the sum of divisors function of n. In this note, we fix a positive integer a and we investigate the positive integers n such that n|a σ(n) − 1. We also show that under a plausible hypothesis related to the distribution of prime numbers there exist infinitely many positive integers n such that n|a σ(n) − 1 holds for all integers a coprime to n.

About this research paper

What this paper is about

Abstract. For a positive integer n let σ(n) be the sum of divisors function of n. In this note, we fix a positive integer a and we investigate the positive integers n such that n|a σ(n) − 1. We also show that under a plausible hypothesis related to the distribution of prime numbers there exist infinitely many positive integers n such that n|a σ(n) − 1 holds for all integers a coprime to n.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract. For a positive integer n let σ(n) be the sum of divisors function of n. In this note, we fix a positive integer a and we investigate the positive integers n such that n|a σ(n) − 1. We also show that under a plausible hypothesis related to the distribution of prime numbers there exist infinitely many positive integers n such that n|a σ(n) − 1 holds for all integers a coprime to n.

Key concepts: Integer (computer science), Mathematics, Combinatorics, Prime (order theory), Prime factor, Discrete mathematics, Computer science, Programming language

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
POSITIVE INTEGERS n SUCH THAT n|a σ(n) − 1 — Research Paper | ScholarLens