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WHEN THE SUM OF ALIQUOTS DIVIDES THE TOTIENT

Published online by Cambridge University Press:  08 January 2008

William D. Banks  and
Florian Luca
William D. Banks
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA (bbanks@math.missouri.edu)
Florian Luca
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de M{é}xico, C.P. 58089, Morelia, Michoacán, Mexico (fluca@matmor.unam.mx)
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Abstract

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Let $\varphi(\cdot)$ be the Euler function and let $\sigma(\cdot)$ be the sum-of-divisors function. In this note, we bound the number of positive integers $n\le x$ with the property that $s(n)=\sigma(n)-n$ divides $\varphi(n)$.

Keywords

Primary 11A25Secondary 11A41sum of divisorsEuler functiondivisibility
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 563 - 569
Copyright
Copyright © Edinburgh Mathematical Society 2007