In mathematics, an abunant number or excessive number is a number n for which σ(n) > 2n. Here σ(n) is the sum-of-divisors function: the sum of all positive divisors of n, including n itself. The value σ(n) − 2n is called the abundance of n. An equivalent definition is that the proper divisors of the number (the divisors except the number itself) sum to more than the number.