omega: Number of Prime Factors
In numbers: Number-Theoretic Functions
omega R Documentation
Number of Prime Factors
Description
Number of prime factors resp. sum of all exponents of prime factors
in the prime decomposition.
Usage
omega(n)
Omega(n)
Arguments
n
Positive integer.
Details
'omega(n)' returns the number of prime factors of 'n' while 'Omega(n)'
returns the sum of their exponents in the prime decomposition.
'omega' and 'Omega' are identical if there are no quadratic factors.
Remark: (-1)^Omega(n) is the Liouville function.
Value
Natural number.
Note
Works well up to 10^9.
See Also
Sigma
Examples
omega(2*3*5*7*11*13*17*19) #=> 8
Omega(2 * 3^2 * 5^3 * 7^4) #=> 10
numbers documentation built on Nov. 23, 2022, 9:06 a.m.
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| omega | R Documentation |
Number of Prime Factors
Description
Number of prime factors resp. sum of all exponents of prime factors in the prime decomposition.
Usage
omega(n) Omega(n)
Arguments
n |
Positive integer. |
Details
'omega(n)' returns the number of prime factors of 'n' while 'Omega(n)' returns the sum of their exponents in the prime decomposition. 'omega' and 'Omega' are identical if there are no quadratic factors.
Remark: (-1)^Omega(n) is the Liouville function.
Value
Natural number.
Note
Works well up to 10^9.
See Also
Sigma
Examples
omega(2*3*5*7*11*13*17*19) #=> 8 Omega(2 * 3^2 * 5^3 * 7^4) #=> 10
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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