Directory: Top/Science/Math/Number_Theory/Factoring/Perfect

Top / Science / Math / Number_Theory / Factoring / Perfect_Numbers /

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.
http://www.unirioja.es/dptos/dmc/jvarona/aliquot.html
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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
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Aliquot Sequences
Results and software from Paul Zimmermann, addressing the Catalan Conjecture and working on the difficult "Lehmer Five" sequences.
http://www.loria.fr/~zimmerma/records/aliquot.html
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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
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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
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Amicable Numbers
Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs.
http://www.shyamsundergupta.com/amicable.htm
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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
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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
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Aliquot
Sequences with initial term up to 10,000, by Christophe Clavier.
http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html
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Perfect Number - from MathWorld
Definitions and references.
http://mathworld.wolfram.com/PerfectNumber.html
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