What does deficient mean in math?

The term "deficient" in mathematics is used in number theory to describe certain types of numbers. In number theory, a deficient number is a positive integer for which the sum of all its proper divisors (the positive integers that divide it evenly, excluding the number itself) is less than the number itself. For example, consider the number 15. The proper divisors of 15 are 1, 3, and 5, and their sum is 1 + 3 + 5 = 9, which is less than 15. Therefore, 15 is a deficient number.

A mathematical definition of a deficient number is given as follows:

A positive integer n is said to be deficient if the sum of its proper divisors, denoted by σ(n), is less than n, i.e., σ(n) < n.

Deficient numbers are contrasted with perfect numbers, which are positive integers for which the sum of all their proper divisors is exactly equal to the number itself, and abundant numbers, which are positive integers for which the sum of all their proper divisors is greater than the number itself.

In summary, a deficient number in mathematics is a positive integer whose sum of proper divisors is less than itself.