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Deficient number
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, ... .
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
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details