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Search Home : Science : Math : Number Theory : Factoring : Perfect Numbers
- Aliquot: Sequences with initial term up to 10,000, by Christophe Clavier.
- Aliquot Sequences: Results and software from Paul Zimmermann, addressing the Catalan Conjecture and working on the difficult "Lehmer Five" sequences.
- Aliquot Sequences: Aliquot sequences arise in iterating the sum-of-divisors function s. Bosma has calculated tables up to start value 50,000 and 80 digits.
- 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.
- Aliquot Sequences: Statistics by Wolfgang Creyaufmueller, including many tables and links to factoring sites and software.
- Amicable Numbers: Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs.
- Cubes of Perfection: From Ivars Peterson's MathTrek column in MAA Online. Curious relationships satisfied by perfect numbers.
- Multiply Perfect Numbers: Up-to-date information on multiperfect numbers and searchable database maintained by Achim Flammenkamp.
- Odd Perfect Numbers - Missing Values: Status of various factorisations that would extend the known area of non-existence of odd perfect numbers, by Kevin Hare.
- 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.
- Perfect Number - from MathWorld: Definitions and references.
- Perfect Numbers: Harry J. Smith's pages of the mathematics behind perfection, aliquot sequences and Mersenne numbers. Includes program listings and e-mail archives.
- Perfect Numbers: A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries.
- Perfect, Amicable and Sociable Numbers: Definitions, links and references of various applications of the sum of divisors function s(n).
- Tables of Aliquot Cycles: Data for various kinds up to 10^12, including unitary, infinitary, exponential, augmented and reduced varieties.
- 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.
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