Reciprocal Sums as a Knowledge Metric: Theory, Computation, and Perfect Numbers
Department or Administrative Unit
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.
Bayless, J. & Klyve, D. (2013). Reciprocal sums as a knowledge metric: Theory, computation, and perfect numbers. The American Mathematical Monthly 120(9), 822-831. DOI: 10.4169/amer.math.monthly.120.09.822
The American Mathematical Monthly
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