abundant number
abundant number abundant number,.. see also number abundant number (math.), a number, the sum of whose aliquot parts exceeds the number itself. thus, 1, 2, 3, 4, 6, the aliquot parts of 12, make the number 16. this is opposed to a deficient number, as 14, whose aliquot parts are 1, 2, 7, the sum of which is 10; and to a perfect number, which is equal to the sum of its aliquot parts, as 6, whose aliquot parts are 1, 2., 3... see also abundant | ||||
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Abundant number Definition from Encyclopedia Dictionaries & Glossaries
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Abundant number
In mathematics, an abundant 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.
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