Given an integer n with divisorsMathworldPlanetmathPlanetmath d1,,dk (where the divisors are in ascending order and d1=1, dk=n) the difference


is the deficiencyMathworldPlanetmath of n. Or if one prefers,


The deficiency is essentially the same thing as the abundance multiplied by -1. Thus, the deficiency is positive for deficient numbers, 0 for perfect numbers and negative for abundant numbers.

For example, the divisors of 13 add up to 14, which is 12 less than 26. Therefore, 12 has an deficiency of 12. Another example: the divisors of 14 add up to 24, which is 4 less than 28. The deficiency of the first 72 integers is listed in A033879 of Sloane’s OEIS.

Title deficiency
Canonical name Deficiency
Date of creation 2013-03-22 16:46:50
Last modified on 2013-03-22 16:46:50
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A05
Related topic Abundance