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单词 AbundantNumber
释义

abundant number


An integer n is an abundant number if the sum of the proper divisors of n is more than n itself, or the sum of all the divisorsMathworldPlanetmathPlanetmath is more than twice n. That is, σ(n)>2n, with σ(n) being the sum of divisors function.

For example, the integer 30. Its proper divisors are 1, 2, 3, 5, 6, 10, 15, which add up to 42.

Multiplying a perfect number by some integer x gives an abundant number (as long as x>1).

Given a pair of amicable numbers, the lesser of the two is abundant, its proper divisors adding up to the greater of the two.

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更新时间:2025/5/4 6:40:44