A generalized divisor problem and the sum of Chowla and Walum

We derive the explicit representation of the integral involving the error term Δ a ( 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 Δ a ( x ) by an elementary method.