Numbers of the form kf(k)-Reference-Cited by-同舟云学术

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Numbers of the form kf(k)

Published:2023-01-30 Issue:05 Volume:19 Page:1191-1204
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Gabdullin Mikhail R.¹^ORCID,Iudelevich Vitalii V.²,Luca Florian³⁴⁵

Affiliation:

1. Steklov Mathematical Institute, Gubkina str., 8, Moscow, 119991, Russia

2. Moscow State University, Leninskie Gory str., 1, Moscow, 119991, Russia

3. School of Maths, Wits University, Private Bag 3, Wits 2050, South Africa

4. Research Group in Algebraic Structures and Applications, King Abdulaziz University, Jeddah, Saudi Arabia

5. Centro de Ciencias Matemáticas UNAM, Morelia, Mexico

Abstract

For a function [Formula: see text], define [Formula: see text]. Let [Formula: see text] be the divisor function, [Formula: see text] be the prime divisor function, and [Formula: see text] be Euler’s totient function. We prove that [Formula: see text] where [Formula: see text].

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042123500586

Reference14 articles.

1. On the number of integers n such that nd(n) ≤ x

2. The distribution of values of the Euler function

3. The Distribution of Values of the Divisor Function d(n)

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