Density modulo 1 of some sequences associated to the functions $\varphi$ and $\sigma$

For any polynomial $G$ with integral coefficients and taking positive values at positive arguments, we prove density modulo 1 of several sequences associated to the Euler and sum of divisors functions evaluated at $G$. More precisely, density modulo 1 of the following sequences with general terms: $\sum_{m\leq n}(\varphi(G(m))/G(m))^\ell$, $\sum_{m\leq n}(G(m)/\sigma(G(m)))^\ell$ and $\sum_{m\leq n}(\varphi(G(m))/\sigma(G(m)))^\ell$ for given $\ell＞0$.