Title

The Humble Sum of Remainders Function

Document Type

Article

Publication Date

10-2005

Publication Title

Mathematics Magazine

Department

Mathematics and Computer Science

Abstract

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.

ISSN

0025-570X