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 $\mathrm{\Omega }$ 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 $\mathrm{\Omega }\left(8\right)$.

$\mathrm{with}\left(\mathrm{NumberTheory}\right)\:$

$\mathrm{NumberOfPrimeFactors}\left(5\right)$

$1$

$\mathrm{NumberOfPrimeFactors}\left(-9\right)$

$2$

$\mathrm{NumberOfPrimeFactors}\left(12\right)$

$3$

$\mathrm{NumberOfPrimeFactors}\left(12\,'\mathrm{distinct}'\right)$

$2$

$\mathrm{\Omega }\left(57\right)$

$2$

$S≔\mathrm{sum}\left(\mathrm{\Omega }\left(f\left(i\right)\right)\,i=1..n\right)$

$S≔\sum _{i=1}^n\mathrm{\Omega }\left(f\left(i\right)\right)$

$\mathrm{eval}\left(S\,\left[\mathrm{`=`}\left(f\,k\mapsto 2\cdot k+1\right)\,n=15\right]\right)$

$21$

$\mathrm{NumberOfPrimeFactors}\left(0\right)$

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.