A correlated digital sum problem associated with sums of three squares

Let ∆(n) be the error term associated with the asymptotic formula for the counting function on the set of numbers that are sums of three squares. By considering ∆(n) as a correlated digital sum and applying the method of H. Delange on ordinary digital sums we give very precise information on the average value of ∆(m) in terms of a periodic continuous nowhere differentiable function having an absolutely convergent Fourier series with coefficients expressed in terms of the Hurwitz zeta function.