On the iteration of the number of divisors without large prime factors
type: Item
instance of: scholarly article
title: On the iteration of the number of divisors without large prime factors
zbMATH Open document ID: 0847.11047
author: Yanyan Li
published in: Journal of Number Theory
publication date: 1996-05-06T00:00:00Z
review text: Let \(d(n)\) denote the number of divisors of \(n\) and \(d(d(n))\) be the iterated divisor function. Among others \textit{E. Heppner} [J. Reine Angew. Math. 265, 176-182 (1974; Zbl 0273.10037)] proved an asymptotic representation for the sum \(\sum_{n\leq x} d(d(n))\). The author considers the same sum, but under the restriction \(p(n)\leq y\leq x\), where \(p(n)\) denotes the greatest prime divisor of \(n\). Further, asymptotic results are given for the sum \[ \sum_{n\leq x} {d(d(n))\over p(n)} \] and similar sums.
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11N25
zbMATH DE Number: 874230
zbMATH Keywords: number of divisors
zbMATH Keywords: iterated divisor function
zbMATH Keywords: asymptotic results
zbMATH Keywords: sums
reviewed by: Ekkehard Krätzel
MaRDI profile type: Publication
full work available at URL: jnth.1996.0034
OpenAlex ID: W2067381698
DOI: 10.1006/JNTH.1996.0034
description: scientific article; zbMATH DE number 874230