Perfect Numbers

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.