proper divisor

If a divisorMathworldPlanetmathPlanetmath d of n (that is, d|n) satisfies 0<|d|<|n|, then d is a proper divisor of n. In the realm of real positive integers, it is usually considered sufficient to list the positive divisors. For example, the proper divisors of 42 are 1, 2, 3, 6, 7, 14, 21.

By restricting the sum of divisors to proper divisors, some n will be less than this sum (deficient numbers, including prime numbersMathworldPlanetmath), some will be equal (perfect numbers) and some will be greater (abundant numbers). The term restricted divisor is sometimes used to further distinguish divisors in the range 1<|d|<|n| (and sometimes it used to mean the same thing as proper divisor). Thus, in our example, the list would be shortened to 2, 3, 6, 7, 14, 21.

Title proper divisor
Canonical name ProperDivisor
Date of creation 2013-03-22 15:52:00
Last modified on 2013-03-22 15:52:00
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 7
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A51
Synonym aliquot part
Synonym restricted divisor