On some problems of Mąkowski–Schinzel and Erdős concerning the arithmetical functions φ and σ

Abstract

Let $\sigma (n)$ denote the sum of positive divisors of the integer $n$, and let $\phi $ denote Euler's function, that is, $\phi (n)$ is the number of integers in the interval $[1,n]$ that are relatively prime to $n$. It has been conjectured by Mąkowski a