number of prime factors counted with multiplicity
The NumberOfPrimeFactors(n) command computes the number of prime factors of the integer n counted with multiplicity.
Every prime number divides 0 evenly, so 0 has infinitely many prime factors. However, for consistency with, for example, the Divisors command, NumberOfPrimeFactors(0) returns an error.
To determine the number of distinct prime divisors of n (that is, without respect to multiplicity), use the distinct = true (or just distinct) option.
Omega and Ω are aliases of NumberOfPrimeFactors.
You can enter the command Omega using either the 1-D or 2-D calling sequence. For example, Omega(8) is equivalent to Ω⁡8.
S ≔ ∑i=1nΩ⁡f⁡i
Error, (in NumberTheory:-NumberOfPrimeFactors) 0 has infinitely many prime factors
The NumberTheory[NumberOfPrimeFactors] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
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