Geodesic
Nonaliquots and Robbins numbers
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
Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 27-32 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm103-1-4
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

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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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

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