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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Nonaliquots and Robbins numbers

### Tom 103 / 2005

Colloquium Mathematicum 103 (2005), 27-32 MSC: Primary 11A25; Secondary 11A41, 11N64. DOI: 10.4064/cm103-1-4

#### Streszczenie

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.

#### Autorzy

• William D. BanksDepartment of Mathematics
University of Missouri
Columbia, MO 65211, U.S.A.
e-mail
• Florian LucaInstituto de Matemáticas