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NumberTheory

 NumberOfPrimeFactors
 number of prime factors counted with multiplicity

 Calling Sequence NumberOfPrimeFactors(n) Omega(n)

Parameters

 n - non-zero integer

Description

 • The NumberOfPrimeFactors command computes the number of prime factors of the integer n counted with multiplicity.
 • Omega is an alias of NumberOfPrimeFactors.

Examples

 > $\mathrm{with}\left(\mathrm{NumberTheory}\right):$
 > $\mathrm{NumberOfPrimeFactors}\left(5\right)$
 ${1}$ (1)
 > $\mathrm{NumberOfPrimeFactors}\left(-9\right)$
 ${2}$ (2)
 > $\mathrm{Ω}\left(57\right)$
 ${2}$ (3)
 > $S≔\sum _{i=1}^{n}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\mathrm{Ω}\left(f\left(i\right)\right)$
 ${S}{≔}{\sum }_{{i}{=}{1}}^{{n}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}{\mathrm{NumberTheory:-Omega}}{}\left({f}{}\left({i}\right)\right)$ (4)
 > $\mathrm{eval}\left(S,\left[f=\left(k→2k+1\right),n=15\right]\right)$
 ${21}$ (5)

Compatibility

 • The NumberTheory[NumberOfPrimeFactors] command was introduced in Maple 2016.
 • For more information on Maple 2016 changes, see Updates in Maple 2016.

 See Also