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