| Directory > Science > Math > Number Theory > Factoring > Perfect Numbers 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.kun.nl/~bosma/research/nuth/ali.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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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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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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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.
http://www.geocities.com/windmill96/fperfect/fperfect.html
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Perfect Numbers
Harry J. Smith's pages of the mathematics behind perfection, aliquot sequences and Mersenne
numbers. Includes program listings and e-mail archives.
http://pw1.netcom.com/~hjsmith/Perfect.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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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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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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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
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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
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Multiperfect Number Search
Sources and binaries of Jason Moxham's searching software.
http://www.maths.soton.ac.uk/~jlm/
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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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Aliquot Sequences
Statistics by Wolfgang Creyaufmueller, including many tables and links to factoring sites and
software.
http://home.t-online.de/home/Wolfgang.Creyaufmueller/aliquote.htm
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