Vol. 10, No. 3, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN (electronic): 2996-220X
ISSN (print): 2996-2196
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