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Aliquot Sequences Juan L. Varona's work on aliquot sequences examines sequences with start values up to 10000, and traces them to large composite values. The Perfect Number Journey A Mathematics Enrichment Workshop introducing perfect numbers. Lessons and exercises extend over several pages. Aimed at interested middle and high school students. Perfect Numbers A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries. Aliquot Sequences Results and software from Paul Zimmermann, addressing the Catalan Conjecture and working on the difficult "Lehmer Five" sequences. Cubes of Perfection From Ivars Peterson's MathTrek column in MAA Online. Curious relationships satisfied by perfect numbers. On a Generalization of Perfect Numbers J. L. Pe introduces perfect numbers relative to an arithmetical function f. Under this scheme, the usual perfect numbers are just one among many species of "f-perfect numbers". Several open problems and examples of perfect number sets are given, as well as a few f-amicable pairs. Amicable Numbers Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs. Multiply Perfect Numbers Up-to-date information on multiperfect numbers and searchable database maintained by Achim Flammenkamp. Tables of Aliquot Cycles Data for various kinds up to 10^12, including unitary, infinitary, exponential, augmented and reduced varieties. Aliquot Sequences with initial term up to 10,000, by Christophe Clavier. |
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