Directory of Perfect Numbers Resources

Home > Science > Math > Number Theory > Factoring > Perfect Numbers

Properties based on the sum-of-divisors function s(n), including perfect and multiperfect numbers, aliquot sequences, amicable pairs and sociable chains.

Subcategories

• Mersenne

Resources in This Category

• 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.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 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.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.

• Aliquot Sequences

  http://www.aliquot.de/aliquote.htm
  Statistics by Wolfgang Creyaufmueller, including many tables and links to factoring sites and software.

• Amicable Numbers

  http://www.shyamsundergupta.com/amicable.htm
  Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs.

• 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 Number - from MathWorld

  http://mathworld.wolfram.com/PerfectNumber.html
  Definitions and references.

• 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.

 

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