We complete the recent research by Akiyama and Kaneko on the higher-order derivative values Φ n (k) (1) of the cyclotomic polynomials. This article focuses on Lehmer's explicit formula of Φ n (k) (1) / Φ n (1) as a polynomial of the Euler and Jordan totient functions over Q . Then we prove Akiyama–Kaneko's conjecture that the polynomials have a specific simple factor.