Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/264
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Examples of Numbers such that Divisor Count divides Phi divides Divisor Sum
The number $264$ has the property that:
- $\map {\sigma_0} {264} \divides \map \phi {264} \divides \map {\sigma_1} {264}$
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
\(\ds \map {\sigma_0} {264}\) | \(=\) | \(\, \ds 16 \, \) | \(\ds \) | $\sigma_0$ of $264$ | ||||||||||
\(\ds \map \phi {264}\) | \(=\) | \(\, \ds 80 \, \) | \(\, \ds = \, \) | \(\ds 5 \times 16\) | $\phi$ of $264$ | |||||||||
\(\ds \map {\sigma_1} {264}\) | \(=\) | \(\, \ds 720 \, \) | \(\, \ds = \, \) | \(\ds 9 \times 80\) | $\sigma_1$ of $264$ |
$\blacksquare$