Abundant number

An abundant number is a number $n$ for which the sum of its proper divisors is greater than $n$ itself. For example, 12 is abundant because the sum of its proper divisors is 1 + 2 + 3 + 4 + 6 = 16 > 12.

Examples

The first 10 abundant numbers are:

12, 18, 20, 24, 30, 36, 40, 42, 48, 54,...

The first 10 odd abundant numbers are:

945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985,...

Properties

There are infinitely many abundant numbers.

Every positive multiple of an abundant number is an abundant number.

Every multiple of a perfect number greater than itself is an abundant number.

See also

Perfect number

Deficient number