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Integers Divisible by the Sum of their Prime Factors

Part of: Elementary number theory

Published online by Cambridge University Press:  21 December 2009

Jean-Marie De Koninck  and
Florian Luca
Jean-Marie De Koninck
Affiliation:
Département de mathématiques, Université Laval, Québec G1K 7P4, Canada. E-mail: jmdk@mat.ulaval.ca
Florian Luca
Affiliation:
Mathematical Institute, UNAM, Ap. Postal 61–3 (Xangari), CP 58 089, Morelia, Michoacán, Mexico. E-mail: fluca@matmor.unam.mx
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Abstract

For each integer n ≥ 2, let β(n) be the sum of the distinct prime divisors of n and let (x) stand for the set of composite integers n ≤ x such that n is a multiple of β(n). Upper and lower bounds are obtained for the cardinality of (x).

MSC classification

Secondary: 11A41: Primes 11A25: Arithmetic functions; related numbers; inversion formulas

Information

Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005 , pp. 69 - 77
Copyright
Copyright © University College London 2005

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