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

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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 $1$

$\blacksquare$