number of distinct prime divisors (Q104120010)

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number of different primes dividing a number

• omega-function
• number of prime divisors
• distinct prime divisors number
• prime divisors number
• number of distinct prime factors

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Language	Label	Description	Also known as
English	number of distinct prime divisors	number of different primes dividing a number	omega-function number of prime divisors distinct prime divisors number prime divisors number number of distinct prime factors

Statements

instance of

additive function

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prime omega function

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subclass of

number of divisors

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defining formula

${\displaystyle \omega (n)=\omega (p_{1}^{\alpha _{1}}p_{2}^{\alpha _{2}}\cdots p_{k}^{\alpha _{k}})=\sum _{p|n}1=k}$

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${\displaystyle \omega (n)=\sum _{p|n}1}$

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in defining formula

${\displaystyle \omega (n)}$

symbol represents

number of distinct prime divisors

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${\displaystyle m|n}$

symbol represents

divides

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${\displaystyle p}$

symbol represents

prime factor

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${\displaystyle n}$

symbol represents

natural number

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calculated from

exponent

in defining formula

${\displaystyle \alpha _{i}}$

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multiplicity

in defining formula

${\displaystyle |}$

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prime factor

in defining formula

${\displaystyle p}$

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less than

number of prime divisors

criterion used

pointwise order

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maintained by WikiProject

WikiProject Mathematics

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is a number of

prime factor

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different from

number of divisors

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Identifiers

MathWorld ID

DistinctPrimeFactors

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OEIS ID

A001221

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Sitelinks

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