# Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/1

## Examples of Numbers such that Divisor Count divides Phi divides Divisor Sum

The number $1$ has the property that:

$\map {\sigma_0} 1 \divides \map \phi 1 \divides \map {\sigma_1} 1$

where:

$\divides$ denotes divisibility
$\sigma_0$ denotes the divisor counting function
$\phi$ denotes the Euler $\phi$ (phi) function
$\sigma_1$ denotes the divisor sum function.

## Proof

 $\ds \map {\sigma_0} 1$ $=$ $\, \ds 1 \,$ $\ds$ $\sigma_0$ of $1$ $\ds \map \phi 1$ $=$ $\, \ds 1 \,$ $\ds$ $\phi$ of $1$ $\ds \map {\sigma_1} 1$ $=$ $\, \ds 1 \,$ $\ds$ $\sigma_1$ of $1$

$\blacksquare$