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Perfect Numbers

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Mersenne (9)

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	Perfect Number - from MathWorld - http://mathworld.wolfram.com/PerfectNumber.html Definitions and references.
	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.
	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.
	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.
	http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html - http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html Sequences with initial term up to 10,000, by Christophe Clavier.

	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.
	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.
	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.

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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