perfect numbers

    Top: Science: Math: Number_Theory: Factoring: Perfect_Numbers:

• - 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.