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2021 On a problem of De Koninck
Tomohiro Yamada
Mosc. J. Comb. Number Theory 10(3): 249-260 (2021). DOI: 10.2140/moscow.2021.10.249

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 k3, and q1|σ(p2), qi+1|σ(qi2) (1ik1), p|σ(qk2).

Citation

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Tomohiro Yamada. "On a problem of De Koninck." Mosc. J. Comb. Number Theory 10 (3) 249 - 260, 2021. https://doi.org/10.2140/moscow.2021.10.249

Information

Received: 31 March 2021; Revised: 31 July 2021; Accepted: 25 August 2021; Published: 2021
First available in Project Euclid: 15 November 2021

Digital Object Identifier: 10.2140/moscow.2021.10.249

Subjects:
Primary: 11A25
Secondary: 05C20‎ , 11A05 , 11A41

Keywords: De Koninck's conjecture , directed acyclic multigraphs , directed multigraphs , radical of an integer , square-free core , sum of divisors

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2021
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