On number of integers representable as a sum of unit fractions. II
type: Item
instance of: scholarly article
title: On number of integers representable as a sum of unit fractions. II
zbMATH Open document ID: 0907.11010
author: H. Yokota
published in: Journal of Number Theory
publication date: 1999-01-24T00:00:00Z
review text: Denote by \(N(n)\) the set of positive integers \(a\) representable in the form \[ a = \sum_{\nu=1}^n {\varepsilon_\nu \over \nu}, \text{ where } \varepsilon \in \{0, 1\}. \] Continuing his research [in \textit{H. Yokota}, Can. Math. Bull. 33, 235-241 (1990; Zbl 0656.10012)], the author proves rather sharp lower and upper estimates for the number of elements in \( N(n) \): For all sufficiently large \(n\), \[ \left( 1 - {5 \log\log n \over \log n} \right) \leq {\#\{N(n)\} \over \log n} < \left( 1 + {1 \over \log n} \right). \] In particular, \( \# \{N(n)\} \sim \log n \).
Mathematics Subject Classification ID: 11D68
Mathematics Subject Classification ID: 11D85
zbMATH DE Number: 1109643
zbMATH Keywords: Egyptian unit fractions
zbMATH Keywords: asymptotic formula for the number of integers representable as sums of unit fractions
reviewed by: Wolfgang Schwarz
MaRDI profile type: Publication
full work available at URL: jnth.1997.2187
OpenAlex ID: W1982958355
cites work: Q3872528
cites work: Q4841598
cites work: Length and denominators of Egyptian fractions. II
cites work: On Number of Integers Representable as Sums of Unit Fractions
DOI: 10.1006/JNTH.1997.2187
description: scientific article; zbMATH DE number 1109643