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Perfect Numbers

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Mersenne@  (9)

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Aliquot - Sequences with initial term up to 10,000, by Christophe Clavier..

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 - 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 - Results and software from Paul Zimmermann, addressing the Catalan Conjecture and working on the difficult "Lehmer Five" sequences..

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 - A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries..

Perfect Numbers - Harry J. Smith's pages of the mathematics behind perfect numbers, aliquot sequences and Mersenne numbers. Includes program listings and e-mail archives..

Tables of Aliquot Cycles - Data for various kinds up to 10^12, including unitary, infinitary, exponential, augmented and reduced varieties..

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