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Infinite families of noncototients

A. Flammenkamp; F. Luca — 2000

Colloquium Mathematicae

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 ${(2^{m} k)}_{m \geq 1}$ consists entirely of noncototients. We then use computations to detect seven such positive integers k.

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