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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 with a unit and primes, PrimeOmega[n] returns .
  • PrimeOmega is a completely additive number theoretic function.
gives the number of prime factors counting multiplicities:
Plot the sequence:
gives the number of prime factors counting multiplicities:
In[1]:=
Click for copyable input
Out[1]=
 
Plot the sequence:
In[1]:=
Click for copyable input
Out[1]=
Evaluate for large arguments:
PrimeOmega works over Gaussian integers:
PrimeOmega threads element-wise over lists:
TraditionalForm formatting:
Number of prime factors of Gaussian integers:
PrimeOmega is a completely additive function:
The number of prime factors can be found using FactorInteger:
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