A remark on sociable numbers of odd order
type: Item
instance of: scholarly article
title: A remark on sociable numbers of odd order
zbMATH Open document ID: 1195.11013
author: Paul Pollack
published in: Journal of Number Theory
publication date: 2010-07-07T00:00:00Z
review text: Let \(s(n)\) be the sum of the proper divisors of the natural number \(n\). The number \(n\) is called sociable if the sequence \(n,s(n),s(s(n)),\dots\) is purely periodic. In this case the period is called the order of sociability of \(n\). Sociable numbers of order \(1\) are called perfect numbers, and sociable numbers of order \(2\) are called amicable numbers. The main result of the paper shows that the number of sociable numbers \(n\leq x\) of order \(k\) is bounded by the quantity \(x/(\log x)^{1+o(1)}\;(x\to\infty)\) in the case of odd and fixed \(k\).
reviewed by: Jonas Šiaulys
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11N25
zbMATH DE Number: 5731631
zbMATH Keywords: sociable number
zbMATH Keywords: sociable chain
zbMATH Keywords: aliquot cycle
zbMATH Keywords: aliquot part
MaRDI profile type: Publication
full work available at URL: j.jnt.2010.03.011
OpenAlex ID: W2047776544
Wikidata QID: Q114157591
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cites work: Bemerkung zu der Arbeit über vollkommene Zahlen in Math. Ann. Bd. 133, S. 431-438 (1957)
DOI: 10.1016/J.JNT.2010.03.011
description: scientific article; zbMATH DE number 5731631