A detailed history of the quest for perfect numbers, from Euclid to their present-day Mersenne discoveries.

Harry J. Smith's pages of the mathematics behind perfection, aliquot sequences and Mersenne numbers. Includes program listings and e-mail archives.

Observations on amicable pairs and their distribution, including Harshad and Happy Amicable pairs.

From Ivars Peterson's MathTrek column in MAA Online. Curious relationships satisfied by perfect numbers.

Data for various kinds up to 10^12, including unitary, infinitary, exponential, augmented and reduced varieties.

Definitions, links and references of various applications of the sum of divisors function s(n).

Results and software from Paul Zimmermann, addressing the Catalan Conjecture and working on the difficult "Lehmer Five" sequences.

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, as well as a few f-amicable pairs.

A Mathematics Enrichment Workshop introducing perfect numbers. Lessons and exercises extend over several pages. Aimed at interested middle and high school students.