Vol. 10, No. 3, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
founded and published with the
scientific support and advice of the
Moscow Institute of
Physics and Technology
 
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Author Index
To Appear
 
Other MSP Journals
On a problem of De Koninck

Tomohiro Yamada

Vol. 10 (2021), No. 3, 249–260
Abstract

Let σ(n) denote the sum of divisors of n and γ(n) denote the product of distinct prime divisors of n. We shall show that, if n1,1782 and σ(n) = (γ(n))2, then there exist odd (not necessarily distinct) primes p,p and (not necessarily odd) distinct primes qi (i = 1,2,,k) such that p,pn, qi2n (i = 1,2,,k), with k 3, and q1|σ(p2), qi+1|σ(qi2) (1 i k 1), p|σ(qk2).

Keywords
sum of divisors, square-free core, radical of an integer, De Koninck's conjecture, directed multigraphs, directed acyclic multigraphs
Mathematical Subject Classification
Primary: 11A25
Secondary: 05C20, 11A05, 11A41
Milestones
Received: 31 March 2021
Revised: 31 July 2021
Accepted: 25 August 2021
Published: 13 September 2021
Authors
Tomohiro Yamada
Center for Japanese Language and Culture
Osaka University
Osaka
Japan