The Korselt set of the square of a prime

Abstract

Let α ∈ ℤ\{0}. A composite number N is said to be an α-Korselt number (Kα-number, for short) if N ≠ α and p - α divides N - α for each prime divisor p of N. The set of all α ∈ ℤ\{0} such that N is a Kα-number is called the Korselt set of N and is denoted by 𝒦𝒮(N). In this paper, we study the Korselt set of q2, where q is prime. We describe in detail how to obtain 𝒦𝒮(q2), compute the cardinality of 𝒦𝒮(q2), and answer some questions related to 𝒦𝒮(q2).