For a non-negative integer n , let s ( n ) denote the digital sum of n . Cheo and Yien proved that for a positive integer x , the sum of the terms of the sequence { s ( n ) : n = 0 , 1 , 2 , … , ( x − 1 ) } is ( 4.5 ) x log x + 0 ( x ) . In this paper we let k be a positive integer and determine that the sum of the sequence { s ( k n ) : n = 0 , 1 , 2 , … , ( x − 1 ) } is also ( 4.5 ) x log x + 0 ( x ) . The constant implicit in the big-oh notation is dependent on k .