On digit sums of multiples of an integer
type: Item
instance of: scholarly article
title: On digit sums of multiples of an integer
zbMATH Open document ID: 1241.11113
author: Cécile Dartyge
author: Pantelimon Stanica
author: Florian Luca
published in: Journal of Number Theory
publication date: 2009-09-15T00:00:00Z
review text: Let \(g\geq 2\) be an integer and \(s_g\) be the sum of digits in base \(g\). In the present paper the authors consider positive integers \(n\) such that \(s_g(n)\) and \(s_g(kn)\) satisfy certain relations for a fixed, or arbitrary positive integer \(k\). In their first result they study the set \[ \mathcal{N}_g=\left\{n:s_g(n)=s_g(kn)\text{ for some } k\neq g^{\ell}\right\}. \] In particular, they can show that the set \(\mathcal{N}_g\) contains all positive integers except for the powers of \(g\). The second result is an answer to a question raised by \textit{W. M. Schmidt} [Studies in pure mathematics, Mem. of P. Turán, 605--622 (1983; Zbl 0523.10030)], concerning for given \(K>0\) the numbers \(n\) such that \(s_2(n)\leq Ks_2(kn)\) for all \(k\geq1\). In particular, for \(x\geq 3\) they show that \[ \#\{n\leq x:s_g(n)\leq Ks_g(kn)\text{ for all }k\geq 1\}\ll\frac{x}{(\log x)^\frac12}. \]
reviewed by: Manfred G. Madritsch
Mathematics Subject Classification ID: 11N25
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 5604006
zbMATH Keywords: sum of digits
zbMATH Keywords: Carmichael lambda function
zbMATH Keywords: Sturdy numbers
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: j.jnt.2009.04.003
OpenAlex ID: W1993969215
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DOI: 10.1016/J.JNT.2009.04.003
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description: scientific article; zbMATH DE number 5604006