1Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A. 2Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58089, Morelia, Michoacán, México
Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 27-32
Let $\varphi(\cdot)$ and $\sigma(\cdot)$ denote the Euler
function and the sum of divisors function, respectively.
We give a lower bound for the number of $m\le x$ for which
the equation $m=\sigma(n)-n$ has no solution. We also show that the set
of positive integers $m$ not of the form $(p-1)/2-\varphi(p-1)$
for some prime number $p$ has a positive lower asymptotic density.
Keywords:
varphi cdot sigma cdot denote euler function sum divisors function respectively lower bound number which equation sigma n has solution set positive integers form p varphi p prime number has positive lower asymptotic density
Affiliations des auteurs :
William D. Banks
1
;
Florian Luca
2
1
Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A.
2
Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58089, Morelia, Michoacán, México
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author = {William D. Banks and Florian Luca},
title = {Nonaliquots and {Robbins} numbers},
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William D. Banks; Florian Luca. Nonaliquots and Robbins numbers. Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 27-32. doi: 10.4064/cm103-1-4
