Noncototients and Nonaliquots
| dc.creator | Banks, William D. | |
| dc.creator | Luca, Florian | |
| dc.date | 2004-09-14 | |
| dc.date.accessioned | 2026-07-07T05:12:06Z | |
| dc.date.available | 2026-07-07T05:12:06Z | |
| dc.description | Let $ϕ(\cdot)$ and $σ(\cdot)$ denote the Euler function and the sum of divisors function, respectively. In this paper, we give a lower bound for the number of positive integers $m\le x$ for which the equation $m=n-ϕ(n)$ has no solution. We also give a lower bound for the number of $m\le x$ for which the equation $m=σ(n)-n$ has no solution. Finally, we show the set of positive integers $m$ not of the form $(p-1)/2-ϕ(p-1)$ for some prime number $p$ has a positive lower asymptotic density. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409231 | |
| dc.identifier | http://arxiv.org/abs/math/0409231 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72467 | |
| dc.subject | Number Theory | |
| dc.subject | 11A25; 11A41, 11N64 | |
| dc.title | Noncototients and Nonaliquots | |
| dc.type | text |