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Science: Math: Number_Theory: Factoring: Perfect_Numbers

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.

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.

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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