Arithmetic functions associated with the infinitary divisors of an integer
type: Item
instance of: scholarly article
title: Arithmetic functions associated with the infinitary divisors of an integer
zbMATH Open document ID: 0774.11006
DOI: 10.1155/S0161171293000456
author: G. L. Cohen
author: Peter Hagis jun.
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1993-11-14T00:00:00Z
full work available at URL: https://eudml.org/doc/46863
review text: The infinitary divisors of a natural number \(n\) are products of its divisors of the form \(p^{y_\alpha 2^\alpha}\), where \(p^y\) is a prime-power component of \(n\) and \(\sum_\alpha y_\alpha 2^\alpha\) (where \(y_\alpha=0\) or 1) is the binary representation of \(y\) [cf. \textit{G. L. Cohen}, Math. Comput. 43, 395--411 (1990; Zbl 0689.10014)]. The authors define ``infinitary'' analogues of such familiar concepts as the greatest common divisor, the Dirichlet convolution, multiplicative functions, Euler's totient, divisor functions and the Möbius function, and exhibit their basic properties.
reviewed by: Pentti Haukkanen
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 179258
zbMATH Keywords: arithmetical functions
zbMATH Keywords: asymptotic formula
zbMATH Keywords: infinitary divisors
zbMATH Keywords: Dirichlet convolution
zbMATH Keywords: multiplicative functions
zbMATH Keywords: Euler's totient
Wikidata QID: Q21147010
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 179258