Curious congruences for cyclotomic polynomials II

We promote the recent research by Akiyama and Kaneko on the higher-order derivative values ${\mathrm{\Phi }}_n^{(k)}(1)$ of the cyclotomic polynomials. This article focuses on Lehmer’s explicit formula of ${\mathrm{\Phi }}_n^{(k)}(1)\mathrm{/}{\mathrm{\Phi }}_n(1)$ 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.