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2013 On the difference between an integer and the sum of its proper divisors
Nichole Davis, Dominic Klyve, Nicole Kraght
Involve 6(4): 493-504 (2013). DOI: 10.2140/involve.2013.6.493


Let σ(n) be the sum of the divisors of n. Although much attention has been paid to the possible values of σ(n)n (the sum of proper divisors), comparatively little work has been done on the possible values of e(n):=σ(n)2n. Here we present some theoretical and computational results on these values. In particular, we exhibit some infinite and possibly infinite families of integers that appear in the image of e(n). We also find computationally all values of n<1020 for which e(n) is odd, and we present some data from our computations. At the end of this paper, we present some conjectures suggested by our computational work.


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Nichole Davis. Dominic Klyve. Nicole Kraght. "On the difference between an integer and the sum of its proper divisors." Involve 6 (4) 493 - 504, 2013.


Received: 7 December 2012; Revised: 18 May 2013; Accepted: 20 May 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1322.11005
MathSciNet: MR3115982
Digital Object Identifier: 10.2140/involve.2013.6.493

Primary: 11A25 , 11Y70

Keywords: computational mathematics , excedents , Sigma Function , sum of divisors

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.6 • No. 4 • 2013
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