In mathematics, an abundant number (also sometimes called an excessive number) is a number n for which the sum of all its positive divisors (including n, the divisor function, σ(n)) is greater than 2n; the value σ(n) - 2n is sometimes called the abundance of n. Abundant numbers were first introduced in Nicomachus' Introductio Arithmetica (circa 100).
An infinite number of both even and odd abundant numbers exist (for example, all multiples of 12 and all odd multiples 945 are abundant); furthermore, every proper multiple of a perfect number and every multiple of an abundant number is abundant. Also, every integer >20161 can be written as the sum of two abundant numbers.
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