Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/420
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Examples of Numbers such that Divisor Count divides Phi divides Divisor Sum
The number $420$ has the property that:
- $\map {\sigma_0} {420} \divides \map \phi {420} \divides \map {\sigma_1} {420}$
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
\(\ds \map {\sigma_0} {420}\) | \(=\) | \(\, \ds 24 \, \) | \(\ds \) | $\sigma_0$ of $420$ | ||||||||||
\(\ds \map \phi {420}\) | \(=\) | \(\, \ds 96 \, \) | \(\, \ds = \, \) | \(\ds 4 \times 24\) | $\phi$ of $420$ | |||||||||
\(\ds \map {\sigma_1} {420}\) | \(=\) | \(\, \ds 1344 \, \) | \(\, \ds = \, \) | \(\ds 14 \times 96\) | $\sigma_1$ of $420$ |
$\blacksquare$