On a divisibility problem (Q2438319)

Let \(\varphi\) and \(\sigma_k\) denote the Euler and generalized divisor functions, respectively. In the paper under review, the authors prove that there are no integers \(n\geq 2\) and \(k\geq 2\) satisfying the divisibility relation \(n^k\mid \varphi(n^k)+\sigma_k(n)\).