## `numlib::Lambda` -- von Mangoldt's function

#### Introduction

`numlib::Lambda``(m)` returns the value of von Mangoldt's function at `m`.

#### Call(s)

`numlib::Lambda(m)`

#### Parameters

`m` | - | arithmetical expression

#### Returns

`numlib::Lambda` returns an arithmetical expression

#### Related Functions

`numlib::ispower`

#### Details

- It is an error if `m` is a number but not a natural number.
- If `m` is not a number, `numlib::Lambda` returns the unevaluated function call.

#### Example 1

`numlib::Lambda` takes on nonzero values only for prime powers:

    >> numlib::Lambda(49)

                                       ln(7)

    >> numlib::Lambda(48)

                                         0

#### Example 2

`numlib::Lambda` returns the function call if its argument is not a number:

    >> numlib::Lambda(3+n^4)

                                              4
                              numlib::Lambda(n  + 3)

#### Background

- The function value of `Lambda` at `m` is defined to be log p if m=p^n for some prime number p and some positive integer n, and to be zero for positive integers that are not prime powers.

#### Changes

- no changes

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