Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/190
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Examples of Numbers such that Divisor Count divides Phi divides Divisor Sum
The number $190$ has the property that:
- $\map {\sigma_0} {190} \divides \map \phi {190} \divides \map {\sigma_1} {190}$
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
\(\ds \map {\sigma_0} {190}\) | \(=\) | \(\, \ds 8 \, \) | \(\ds \) | $\sigma_0$ of $190$ | ||||||||||
\(\ds \map \phi {190}\) | \(=\) | \(\, \ds 72 \, \) | \(\, \ds = \, \) | \(\ds 9 \times 8\) | $\phi$ of $190$ | |||||||||
\(\ds \map {\sigma_1} {190}\) | \(=\) | \(\, \ds 360 \, \) | \(\, \ds = \, \) | \(\ds 5 \times 72\) | $\sigma_1$ of $190$ |
$\blacksquare$