The Humble Sum of Remainders Function
Mathematics and Computer Science
Given an integer n, define the sum of remainders function such that when n is input to the function, the output is the sum of the the remainders obtained by dividing n successively by 1, 2, ..., n. This paper describes two uses of the sum of remainders function: 1) It provides a simple alternative characterization of perfect numbers, and 2) together with the more famous sum of divisors function, it helps give an expression for the sums of powers of the first n positive integers.
Spivey, M Z. "The Humble Sum of Remainders Function." Mathematics Magazine. 78.4 (2005): 300-304. Print.