Arithmetic Functions

An arithmetic function is a function ` ZZ^+ \rightarrow S ` where `S \subseteq RR \subseteq CC `.  They try to capture the essence of various properties of positive whole numbers.

Examples
The constant ` 1 ` function maps every  n  to the number 1.

The identity function ` I ` maps every  n  to itself.

Möbius function ` \mu `

The unit function ` \delta_1 ` (or ` \epsilon ` function)

Euler's totient function ` \phi `

Number of divisors ` \tau `

Sum of divisors ` \tau `