Deficient number


In number theory, a deficient number or defective number is a number n for which the sum of divisors σ<2n, or, equivalently, the sum of proper divisors s<n. The value 2n − σ is called the number's deficiency.

Examples

The first few deficient numbers are:
As an example, consider the number 21. Its proper divisors are 1, 3 and 7, and their sum is 11. Because 11 is less than 21, the number 21 is deficient. Its deficiency is 2 × 21 − 32 = 10.

Properties

Closely related to deficient numbers are perfect numbers with σ = 2n, and abundant numbers with σ > 2n. The natural numbers were first classified as either deficient, perfect or abundant by Nicomachus in his Introductio Arithmetica.