Infinite families of noncototients
Volume 86 / 2000
Colloquium Mathematicum 86 (2000), 37-41
DOI: 10.4064/cm-86-1-37-41
Abstract
For any positive integer $n$ let ϕ(n) be the Euler function of n. A positive integer $n$ is called a noncototient if the equation x-ϕ(x)=n has no solution x. In this note, we give a sufficient condition on a positive integer k such that the geometrical progression $(2^mk)_{m ≥ 1}$ consists entirely of noncototients. We then use computations to detect seven such positive integers k.
