A generalized divisor problem and the sum of Chowla and Walum

We derive the explicit representation of the integral involving the error term Δa(x)Δa(x) in a generalized divisor problem by using the sum of Chowla and Walum. We give a new estimate of the sum of Chowla and Walum. We also derive an asymptotic formula for the mean square of the error term in the mean value of Δa(x)Δa(x) by an elementary method.