Title

Reciprocal Sums as a Knowledge Metric: Theory, Computation, and Perfect Numbers

Document Type

Article

Department or Administrative Unit

Mathematics

Publication Date

2013

Abstract

We first provide a short survey of reciprocal sums. We discuss some of the history of their computation and application, show how they are applied in various modern contexts, and discuss some ways that their values are computed. We give an example of computing a reciprocal sum by providing (we believe) the first computation of the sum of the reciprocals of perfect numbers. Second, we introduce a new use for reciprocal sums; that is, they can be used as a knowledge metric to classify the current state of number theorists’ understanding of a given class of integers.

Comments

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Journal

The American Mathematical Monthly

Copyright

Copyright © 2013 The Mathematical Association of America