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Top: Science: Math: Number_Theory: Factoring: Perfect_Numbers:
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    • Aliquot - - Sequences with initial term up to 10,000, by Christophe Clavier.
    • 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.
    • Aliquot Sequences - - Statistics by Wolfgang Creyaufmueller, including many tables and links to factoring sites and software.
    • 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.
    • Aliquot Sequences - - Results and software from Paul Zimmermann, addressing the Catalan Conjecture and working on the difficult "Lehmer Five" sequences.
    • Amicable Numbers - - Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs.
    • Cubes of Perfection - - From Ivars Peterson's MathTrek column in MAA Online. Curious relationships satisfied by perfect numbers.
    • Multiply Perfect Numbers - - Up-to-date information on multiperfect numbers and searchable database maintained by Achim Flammenkamp.
    • Odd Perfect Numbers - Missing Values - - Status of various factorisations that would extend the known area of non-existence of odd perfect numbers, by Kevin Hare.
    • 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.
    • Perfect Number - from MathWorld - - Definitions and references.
    • 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.
    • Perfect Numbers - - A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries.
    • Perfect Numbers - - Harry J. Smith's pages of the mathematics behind perfect numbers, aliquot sequences and Mersenne numbers. Includes program listings and e-mail archives.
    • Tables of Aliquot Cycles - - Data for various kinds up to 10^12, including unitary, infinitary, exponential, augmented and reduced varieties.

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    Perfect Numbers - Science - Math - Number Theory - Factoring - Perfect Numbers
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