  Let $k\geq 1$ be an integer. Let $\delta_k(n)$ denote the maximum divisor of
$n$ which is co-prime to $k$. We study the error term of the general $m$-th
Riesz mean of the arithmetical function $\delta_k(n)$ for any positive integer
$m \ge 1$, namely the error term $E_m(x)$ where
  \[ \frac{1}{m!}\sum_{n \leq x}\delta_k(n) \left( 1-\frac{n}{x} \right)^m =
M_{m, k}(x) + E_{m, k}(x). \] We establish a non-trivial upper bound for $\left
| E_{m, k} (x) \right |$, for any integer $m\geq 1$.
