Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/15

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

The number $15$ has the property that:

$\map {\sigma_0} {15} \divides \map \phi {15} \divides \map {\sigma_1} {15}$

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

\(\ds \map {\sigma_0} {15}\)

\(=\)

\(\, \ds 4 \, \)

\(\ds \)

$\sigma_0$ of $15$

\(\ds \map \phi {15}\)

\(=\)

\(\, \ds 8 \, \)

\(\, \ds = \, \)

\(\ds 2 \times 4\)

$\phi$ of $15$

\(\ds \map {\sigma_1} {15}\)

\(=\)

\(\, \ds 24 \, \)

\(\, \ds = \, \)

\(\ds 3 \times 8\)

$\sigma_1$ of $15$

$\blacksquare$