Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/70
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Examples of Numbers such that Divisor Count divides Phi divides Divisor Sum
The number $70$ has the property that:
- $\map {\sigma_0} {70} \divides \map \phi {70} \divides \map {\sigma_1} {70}$
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
\(\ds \map {\sigma_0} {70}\) | \(=\) | \(\, \ds 8 \, \) | \(\ds \) | $\sigma_0$ of $70$ | ||||||||||
\(\ds \map \phi {70}\) | \(=\) | \(\, \ds 24 \, \) | \(\, \ds = \, \) | \(\ds 3 \times 8\) | $\phi$ of $70$ | |||||||||
\(\ds \map {\sigma_1} {70}\) | \(=\) | \(\, \ds 144 \, \) | \(\, \ds = \, \) | \(\ds 6 \times 24\) | $\sigma_1$ of $70$ |
$\blacksquare$