proper divisor

If a divisor $d$ of $n$ (that is, $d|n$) satisfies , 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 numbers), 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 (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