Factoring Perfect Numbers
You have found the way to Perfect Numbers on Factoring:
- Mersenne@ (9)
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. Help build the largest human-edited directory on the web.