Perfect Numbers Factoring Number Theory

Perfect Numbers Factoring Number Theory

Perfect Numbers

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

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- Up-to-date information on multiperfect numbers and searchable database maintained by Achim Flammenkamp.
- 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,
- Definitions, links and references of various applications of the sum of divisors function s(n).
- Status of various factorisations that would extend the known area of non-existence of odd perfect numbers, by Kevin Hare.
- Aliquot sequences arise in iterating the sum-of-divisors function s. Bosma has calculated tables up to start value 50,000 and 80 digits.
- Sequences with initial term up to 10,000, by Christophe Clavier.
- Harry J. Smith's pages of the mathematics behind perfect numbers, aliquot sequences and Mersenne numbers. Includes program listings and e-mail archives.
- A Mathematics Enrichment Workshop introducing perfect numbers. Lessons and exercises extend over several pages. Aimed at interested middle and high school students.
- Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs.
- Data for various kinds up to 10^12, including unitary, infinitary, exponential, augmented and reduced varieties.
- Definitions and references.
- From Ivars Peterson's MathTrek column in MAA Online. Curious relationships satisfied by perfect numbers.

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