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Perfect Numbers
  Science > Math > Number Theory > Factoring > Perfect Numbers   Go to Directory Home: [English]  [English]  

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Mersenne (9)
Web Pages
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  Perfect Numbers http://www-history.mcs.st-and.ac.uk/history/HistTopics/Perfect_numbers.html
A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries.
  Perfect Number - from MathWorld http://mathworld.wolfram.com/PerfectNumber.html
Definitions and references.
  Aliquot Sequences http://www.loria.fr/~zimmerma/records/aliquot.html
Results and software from Paul Zimmermann, addressing the Catalan Conjecture and working on the difficult "Lehmer Five" sequences.
  Aliquot Sequences http://www.unirioja.es/dptos/dmc/jvarona/aliquot.html
Juan L. Varona's work on aliquot sequences examines sequences with start values up to 10000, and traces them to large composite values.
  Aliquot http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html
Sequences with initial term up to 10,000, by Christophe Clavier.
  Aliquot Sequences http://www.aliquot.de/aliquote.htm
Statistics by Wolfgang Creyaufmueller, including many tables and links to factoring sites and software.
  Cubes of Perfection http://www.maa.org/mathland/mathtrek_5_18_98.html
From Ivars Peterson's MathTrek column in MAA Online. Curious relationships satisfied by perfect numbers.
  Aliquot Sequences http://www.math.ru.nl/~bosma/research/nuth/ali.html
Aliquot sequences arise in iterating the sum-of-divisors function s. Bosma has calculated tables up to start value 50,000 and 80 digits.
  Multiply Perfect Numbers http://wwwhomes.uni-bielefeld.de/achim/mpn.html
Up-to-date information on multiperfect numbers and searchable database maintained by Achim Flammenkamp.
  Perfect Numbers http://www.geocities.com/hjsmithh/Perfect.html
Harry J. Smith's pages of the mathematics behind perfect numbers, aliquot sequences and Mersenne numbers. Includes program listings and e-mail archives.
  Amicable Numbers http://www.shyamsundergupta.com/amicable.htm
Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs.
  Tables of Aliquot Cycles http://amicable.homepage.dk/tables.htm
Data for various kinds up to 10^12, including unitary, infinitary, exponential, augmented and reduced varieties.
  On a Generalization of Perfect Numbers http://www.geocities.com/windmill96/fperfect/fperfect.html
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.

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