Editing Deficient number (section)

{{short description|Number that is more than the sum of its proper divisors}}
[[File:Deficient number Cuisenaire rods 8.png|thumb|Demonstration, with [[Cuisenaire rods]], of the deficiency of the number 8]]

In [[number theory]], a '''deficient number''' or '''defective number''' is a [[positive integer]] {{mvar|n}} for which the [[Divisor function#Definition|sum of divisors]] of {{mvar|n}} is less than {{math|2''n''}}.  Equivalently, it is a number for which the sum of [[proper divisor]]s (or [[aliquot sum]]) is less than {{mvar|n}}.  For example, the proper divisors of 8 are {{nowrap|1, 2, and 4}}, and their sum is less than 8, so 8 is deficient.

Denoting by {{math|''σ''(''n'')}} the sum of divisors, the value {{math|2''n'' – ''σ''(''n'')}} is called the number's '''deficiency'''.  In terms of the aliquot sum {{math|''s''(''n'')}}, the deficiency is {{math|''n'' – ''s''(''n'')}}.