Perfect, Amicable and Sociable Numbers
Definitions, links and references of various applications of the sum of divisors function s(n).
http://xraysgi.ims.uconn.edu:8080/amicable.html
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.
http://home1.pacific.net.sg/%7Enovelway/MEW2/lesson1.html
Perfect Numbers
A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries.
http://www-history.mcs.st-and.ac.uk/history/HistTopics/Perfect_numbers.html
Cubes of Perfection
From Ivars Peterson's MathTrek column in MAA Online. Curious relationships satisfied by perfect numbers.
http://www.maa.org/mathland/mathtrek_5_18_98.html
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,
http://www.geocities.com/windmill96/fperfect/fperfect.html
Amicable Numbers
Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs.
http://www.shyamsundergupta.com/amicable.htm
Multiply Perfect Numbers
Up-to-date information on multiperfect numbers and searchable database maintained by Achim Flammenkamp.
http://wwwhomes.uni-bielefeld.de/achim/mpn.html
Tables of Aliquot Cycles
Data for various kinds up to 10^12, including unitary, infinitary, exponential, augmented and reduced varieties.
http://amicable.homepage.dk/tables.htm
Aliquot
Sequences with initial term up to 10,000, by Christophe Clavier.
http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html
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.
http://www.math.uwaterloo.ca/~kghare/ODDPERFECT/MissingValues.html
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.
http://www.math.ru.nl/~bosma/research/nuth/ali.html
Last Updated: 2005-02-03 23:09:11
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