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单词 NumberOfDistinctPrimeFactorsFunction
释义

number of distinct prime factors function


The number of distinct prime factors function ω(n) counts how many distinct prime factors n has. Expressing n as

n=i=1kpiai,

where the pi are distinct primes, there being k of them, and the ai are positive integers (not necessarily distinct), then ω(n)=k.

Obviously for a prime p it follows that ω(p)=1. When n is a squarefreeMathworldPlanetmath number, then Ω(n)=ω(n), where Ω(n) is the number of (nondistinct) prime factorsMathworldPlanetmath functionMathworldPlanetmath (http://planetmath.org/NumberOfNondistinctPrimeFactorsFunction). Otherwise, Ω(n)>ω(n).

ω(n) is an additive functionMathworldPlanetmath, and it can be used to define a multiplicative functionMathworldPlanetmath like the Möbius function μ(n)=(-1)ω(n) (as long as n is squarefree).

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更新时间:2025/5/4 3:02:16