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Mathematica > Mathematics and Algorithms > Number Theory > Prime Numbers > PrimeOmega >

BUILT-IN MATHEMATICA SYMBOL

PrimeOmega

PrimeOmega[n]
gives the number of prime factors counting multiplicities

in n.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

PrimeOmega[n, GaussianIntegers->True] gives the number of Gaussian prime factors in n.

gives the number of prime factors counting multiplicities:

Plot the sequence:

gives the number of prime factors counting multiplicities:

Out[1]=

Plot the sequence:

Out[1]=

Evaluate for large arguments:

PrimeOmega works over Gaussian integers:

PrimeOmega threads element-wise over lists:

Number of prime factors of Gaussian integers:

PrimeOmega is a completely additive function:

The number of prime factors can be found using FactorInteger: