Let ψ denote the Dedekind totient function by id ∗ μ^2, where μ is the Möbius function. We establish the asymptotic formula of the general kth Riesz mean of the arithmetical function n/ψ(n) for any positive integer k ≥ 2; namely 1/k!Σ__〈n ≤x〉n/(ψ(n))(1-n/x)^k=(ζ(4)h(1))/( (k + 1)!ζ(2))x+O(1/kexp(-C((logx)^〈1/3〉)/((log logx)^〈1/3〉))) with h(1)=П__p(1+1/(p^3(1+1/p))-1/(p^4(1+1/p))). Assuming that the Riemann Hypothesis is true, then the error term of the above function can be estimated as O(k^〈−1〉x^〈−1/(2+δ)〉 for any small positive constant δ.