Numbers such that Divisor Count divides Phi divides Divisor Sum/Examples/210
Jump to navigation
Jump to search
Examples of Numbers such that Divisor Count divides Phi divides Divisor Sum
The number $210$ has the property that:
- $\map {\sigma_0} {210} \divides \map \phi {210} \divides \map {\sigma_1} {210}$
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
\(\ds \map {\sigma_0} {210}\) | \(=\) | \(\, \ds 16 \, \) | \(\ds \) | $\sigma_0$ of $210$ | ||||||||||
\(\ds \map \phi {210}\) | \(=\) | \(\, \ds 48 \, \) | \(\, \ds = \, \) | \(\ds 3 \times 16\) | $\phi$ of $210$ | |||||||||
\(\ds \map {\sigma_1} {210}\) | \(=\) | \(\, \ds 576 \, \) | \(\, \ds = \, \) | \(\ds 12 \times 48\) | $\sigma_1$ of $210$ |
$\blacksquare$
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $210$