Solutions of the equation d (kn) = ϕ (ϕ (n)) - Zahra, Amroune; Djamel, Bellaouar; Abdelmadjid, Boudaoud (Jordan Journal of Mathematics and Statistics, 2024)
Let d(n) and ϕ (n) denote the number of positive integers dividing the positive integer n and the Euler’s phi function representing the numbers less than and prime to n, respectively. In this paper, we determine all solutions of the equation d(n) = ϕ (ϕ (n)) and we prove that the equation d(kn) = ϕ (ϕ (n)) has a finite number of solutions for any k ≥ 1. Further, we characterize all solutions of the last equation when k is prime.