On some friends of the sociable numbers
type: Item
instance of: scholarly article
title: On some friends of the sociable numbers
zbMATH Open document ID: 1227.11016
author: Paul Pollack
published in: Monatshefte für Mathematik
publication date: 2011-03-31T00:00:00Z
review text: Let \(s(n):=\sum_{d\mid n,d<n}d\), \(s_0(n)=n\) and for \(k>0\) define \(s_k(n)=s(s_{k-1}(n))\) if \(s_{k-1}(n)>0\). A social number \(n\) satisfies \(s_k(n)=n\) for some \(k\). Let \(k\geq 1\). The author proves that the set of \(n\) for which \(s_k(n)\) exists and is a multiple of \(n\) has density zero. The set of \(n\) for which \(s_k(n)\) exists and is a divisor of \(n\) has density zero.
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 5872794
zbMATH Keywords: sociable numbers
MaRDI profile type: Publication
full work available at URL: s00605-010-0240-x
OpenAlex ID: W2071754076
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DOI: 10.1007/S00605-010-0240-X
description: scientific article; zbMATH DE number 5872794