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单词 ColossallyAbundantNumber
释义

colossally abundant number


An integer n is a colossally abundant number if there is an exponent ϵ>1 such that the sum of divisorsMathworldPlanetmathPlanetmath of n divided by n raised to that exponent is greater than or equal to the sum of divisors of any other integer k>1 divided by k raised to that same exponent. That is,

σ(n)nϵσ(k)kϵ,

with σ(n) being the sum of divisors function.

The first few colossally abundant numbers are 1, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320. The index of a colossally abundant number is equal to the number of its nondistinct prime factorsMathworldPlanetmath, that is to say that for the ith colossally abundant number ci the equality i=Ω(ci) is true.

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更新时间:2025/5/4 13:21:15