Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/616

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

The number $616$ has the property that:

$\map {\sigma_0} {616} \divides \map \phi {616} \divides \map {\sigma_1} {616}$

where:

$\divides$ denotes divisibility

$\sigma_0$ denotes the divisor count function

$\phi$ denotes the Euler $\phi$ (phi) function

$\sigma_1$ denotes the divisor sum function.

Proof

\(\ds \map {\sigma_0} {616}\)

\(=\)

\(\, \ds 16 \, \)

\(\ds \)

$\sigma_0$ of $616$

\(\ds \map \phi {616}\)

\(=\)

\(\, \ds 240 \, \)

\(\, \ds = \, \)

\(\ds 15 \times 16\)

$\phi$ of $616$

\(\ds \map {\sigma_1} {616}\)

\(=\)

\(\, \ds 1440 \, \)

\(\, \ds = \, \)

\(\ds 6 \times 240\)

$\sigma_1$ of $616$

$\blacksquare$