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PrimeOmega

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

in n.

MORE INFORMATION

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.

PrimeOmega is a completely additive number theoretic function.

Basic Examples (2)

gives the number of prime factors counting multiplicities:

Plot the sequence:

Properties & Relations (2)

PrimeNu LiouvilleLambda FactorInteger

Demonstrations with PrimeOmega (Wolfram Demonstrations Project)

New in 7

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