On the Riesz means of $delta_k(n)$

Let $kgeq 1$ 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 $mgeq 1$.