Cyclotomic Polynomials, Symmetric Polynomials, and a Generalization of Euler's Totient Function

Abstract

SummaryWe introduce a generalization of Euler's totient function that, when applied to an integer n ≥ 2, can be written as a polynomial in the prime factors of n. We then show how cyclotomic and complete homogeneous symmetric polynomials appear as factors of these polynomials when n has at most two distinct prime divisors.