In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number: its proper divisors are 1, 2, 3, 4 and 6, and their sum 16 is larger than 12. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example.

Definition and examples