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# Abundant number

In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. [1]

## Aliquot sum

In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself.

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Deficient number

In number theory, a deficient or deficient number is a number n for which the sum of divisors &sigma;(n) for all sufficiently large n.Sándor et al (2006) p.108.

## Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

## Divisor function

In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.

## Friendly number

In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Introduction to Arithmetic

The book Introduction to Arithmetic (Ἀριθμητικὴ εἰσαγωγή, Arithmetike eisagoge) is the only extant work on mathematics by Nicomachus (60&ndash;120 AD).

## Journal of Number Theory

The Journal of Number Theory is a mathematics journal that publishes a broad spectrum of original research in number theory.

## Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

## Natural density

In number theory, natural density (or asymptotic density or arithmetic density) is one of the possibilities to measure how large a subset of the set of natural numbers is.

## Nicomachus

Nicomachus of Gerasa (Νικόμαχος; c. 60 &ndash; c. 120 AD) was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek.

## Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

## Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

## Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

## Quasiperfect number

In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the divisor function σ(n)) is equal to 2n + 1.

## Semiperfect number

In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors.

## Simon Stevin (journal)

Simon Stevin was a Dutch language academic journal in pure and applied mathematics, or Wiskunde as the field is known in Dutch.

## Weird number

In number theory, a weird number is a natural number that is abundant but not semiperfect.

## References

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