ON THE SUMS OF COMPLEMENTARY DIVISORS-Reference-Cited by-同舟云学术

ON THE SUMS OF COMPLEMENTARY DIVISORS

Published:2007-12 Issue:04 Volume:03 Page:635-648
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BECHEANU MIRCEA¹,LUCA FLORIAN²,SHPARLINSKI IGOR E.³

Affiliation:

1. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania

2. Instituto de Matemáticas, Universidad Nacional Autónoma de Mexico, C.P. 58089, Morelia, Michoacán, Mexico

3. Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

Abstract

In this paper, we study various arithmetic properties of d + n/d, where d runs through all the τ(n) positive divisors of n. For example, denoting by ϖ(n) the number of prime values among these sums, we study how often ϖ(n) > 0 and also ϖ(n) = τ(n), and we also evaluate the average value of ϖ(n). We estimate some character sums with d + n/d and study the distribution of quadratic nonresidues and primitive roots among these sums on average over n ≤ x.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042107001152

Reference13 articles.

1. The Prime k-Tuplets Conjecture on Average

2. Values of the Euler Function in Various Sequences

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4. Primes represented by irreducible polynomials in one variable

5. On a problem of Oppenheim concerning “factorisatio numerorum”

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1. On the values of the divisor function;Monatshefte für Mathematik;2007-11-05