Deficient number
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In mathematics, a deficient number or defective number is a number n for which σ(n) < 2n. Here σ(n) is the divisor function: the sum of all positive divisors of n, including n itself. The value 2n − σ(n) is called the deficiency of n.
Deficient numbers were first introduced in Nicomachus' Introductio Arithmetica (circa 100). The first few deficient numbers are 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, ... Template:OEIS.
An infinite number of both even and odd deficient numbers exist. For example, all prime numbers, all prime powers and all proper divisors of deficient or perfect numbers are deficient.
See also
External links
- The Prime Glossary: Deficient number (http://primes.utm.edu/glossary/page.php?sort=DeficientNumber)
- MathWorld: Deficient number (http://mathworld.wolfram.com/DeficientNumber.html)de:Defiziente Zahl
es:Número defectivo fr:Nombre déficient he:מספר חסר it:Numero deficiente nl:Onvolmaakt getal pt:Número defectivo ru:Недостаточные числа sl:Nezadostno število sv:Defekt tal