Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/56

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

The number $56$ has the property that:

$\map {\sigma_0} {56} \divides \map \phi {56} \divides \map {\sigma_1} {56}$

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

\(\ds \map {\sigma_0} {56}\)

\(=\)

\(\, \ds 8 \, \)

\(\ds \)

$\sigma_0$ of $56$

\(\ds \map \phi {56}\)

\(=\)

\(\, \ds 24 \, \)

\(\, \ds = \, \)

\(\ds 3 \times 8\)

$\phi$ of $56$

\(\ds \map {\sigma_1} {56}\)

\(=\)

\(\, \ds 120 \, \)

\(\, \ds = \, \)

\(\ds 5 \times 24\)

$\sigma_1$ of $56$

$\blacksquare$