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Prime omega function

In number theory, the prime omega functions ω ( n ) {\displaystyle \omega (n)} and Ω ( n ) {\displaystyle \Omega (n)} count the number of prime factors of a natural number n {\displaystyle n} . The number of distinct prime factors is assigned to ω ( n ) {\displaystyle \omega (n)} (little omega), while Ω ( n ) {\displaystyle \Omega (n)} (big omega) counts…

Properties and relations, Average order and summatory functions & Dirichlet series

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Properties and relations

AdditiveDivisor functionSquarefreeMöbius functionPrime power
16 related topics

Average order and summatory functions

PrimePrimorialPower of 2Iverson bracketFactorial moments
5 related topics

Dirichlet series

Dirichlet seriesRiemann zeta functionEuler productPrime zeta functionHarmonic number
5 related topics

The distribution of the difference of prime omega functions

Erdős–Kac theorem
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Properties and relations

Average order and summatory functions

Dirichlet series

The distribution of the difference of prime omega functions

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Prime omega function

Nodes36
Edges35
Triples0
Avg. degree1.94
Density0.055556
Components1

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displaystyle omega prime function functions number distinct series primes related given factors summatory dirichlet see additive sum theory form average

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