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The sum of the divisors of a positive integer is one of the most interesting concepts in multiplicative number theory, while the number of ways of expressing a number as a sum is a primary topic in additive number theory. In this article, we describe some of the surprising connections between and similarities of these two concepts.

The notions of pentagonal numbers and partitions can be understood by students at the precalculus level, and should work well in a first course in programming for high school or college students. Presents opportunities to conjecture properties of partitions from a computer program. (Contains 14 references.) (Author/ASK)