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=k∏i=1piai, |
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 squarefree number, then Ω(n)=ω(n), where Ω(n) is the number of (nondistinct) prime factors
function
(http://planetmath.org/NumberOfNondistinctPrimeFactorsFunction). Otherwise, Ω(n)>ω(n).
ω(n) is an additive function, and it can be used to define a multiplicative function
like the Möbius function μ(n)=(-1)ω(n) (as long as n is squarefree).
Title | number of distinct prime factors function |
---|---|
Canonical name | NumberOfDistinctPrimeFactorsFunction |
Date of creation | 2013-03-22 16:06:52 |
Last modified on | 2013-03-22 16:06:52 |
Owner | CompositeFan (12809) |
Last modified by | CompositeFan (12809) |
Numerical id | 9 |
Author | CompositeFan (12809) |
Entry type | Definition |
Classification | msc 11A25 |
Related topic | NumberOfNondistinctPrimeFactorsFunction |
Related topic | 2omeganLeTaunLe2Omegan |