Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/570

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

The number $570$ has the property that:

$\map {\sigma_0} {570} \divides \map \phi {570} \divides \map {\sigma_1} {570}$

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

\(\ds \map {\sigma_0} {570}\)

\(=\)

\(\, \ds 16 \, \)

\(\ds \)

$\sigma_0$ of $570$

\(\ds \map \phi {570}\)

\(=\)

\(\, \ds 144 \, \)

\(\, \ds = \, \)

\(\ds 9 \times 16\)

$\phi$ of $570$

\(\ds \map {\sigma_1} {570}\)

\(=\)

\(\, \ds 1440 \, \)

\(\, \ds = \, \)

\(\ds 10 \times 144\)

$\sigma_1$ of $570$

$\blacksquare$