Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/78

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

The number $78$ has the property that:

$\map {\sigma_0} {78} \divides \map \phi {78} \divides \map {\sigma_1} {78}$

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

\(\ds \map {\sigma_0} {78}\)

\(=\)

\(\, \ds 8 \, \)

\(\ds \)

$\sigma_0$ of $78$

\(\ds \map \phi {78}\)

\(=\)

\(\, \ds 24 \, \)

\(\, \ds = \, \)

\(\ds 3 \times 8\)

$\phi$ of $78$

\(\ds \map {\sigma_1} {78}\)

\(=\)

\(\, \ds 168 \, \)

\(\, \ds = \, \)

\(\ds 7 \times 24\)

$\sigma_1$ of $78$

$\blacksquare$