## `numlib::Omega` -- Number of prime divisors (with multiplicity)

#### Introduction

`numlib::Omega``(a)` returns, for a given positive integer `a`, the finite sum sum(alpha(p,a)), where p runs through all primes, and alpha(p,a) denotes the highest exponent for which p^alpha divides `a`.

#### Call(s)

`numlib::Omega(a)`

#### Parameters

`a` | - | positive integer

#### Returns

`numlib::Omega` returns a positive integer.

#### Related Functions

`numlib::numprimedivisors`

#### Details

- `numlib::Omega` returns the function call with evaluated argument if the argument is not a number.
- `numlib::Omega` returns an error if the argument evaluates to a number of wrong type.

#### Example 1

In contrast to `numlib::numprimedivisors`, the prime factor 2 of 120 is counted thrice:

    >> numlib::Omega(120)

                                         5

The same happens here:

    >> numlib::Omega(8)

                                         3

#### Changes

- no changes

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