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(Q104120010)
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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
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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
ω
(
n
)
=
ω
(
p
1
α
1
p
2
α
2
⋯
p
k
α
k
)
=
∑
p
|
n
1
=
k
{\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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ω
(
n
)
=
∑
p
|
n
1
{\displaystyle \omega (n)=\sum _{p|n}1}
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in defining formula
ω
(
n
)
{\displaystyle \omega (n)}
symbol represents
number of distinct prime divisors
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m
|
n
{\displaystyle m|n}
symbol represents
divides
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p
{\displaystyle p}
symbol represents
prime factor
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n
{\displaystyle n}
symbol represents
natural number
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calculated from
exponent
in defining formula
α
i
{\displaystyle \alpha _{i}}
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multiplicity
in defining formula
|
{\displaystyle |}
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prime factor
in defining formula
p
{\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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