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

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.

For a number n=u p₁^k₁ p_m^k_m with u a unit and p_i primes, PrimeOmega[n] returns k₁++k_m.

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:

Plot the sequence:

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:

Number of prime factors can be found using FactorInteger: