Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/1
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Examples of Numbers such that Divisor Count divides Phi divides Divisor Sum
The number $1$ has the property that:
- $\map {\sigma_0} 1 \divides \map \phi 1 \divides \map {\sigma_1} 1$
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
\(\ds \map {\sigma_0} 1\) | \(=\) | \(\, \ds 1 \, \) | \(\ds \) | $\sigma_0$ of $1$ | ||||||||||
\(\ds \map \phi 1\) | \(=\) | \(\, \ds 1 \, \) | \(\ds \) | $\phi$ of $1$ | ||||||||||
\(\ds \map {\sigma_1} 1\) | \(=\) | \(\, \ds 1 \, \) | \(\ds \) | $\sigma_1$ of $1$ |
$\blacksquare$