Ore Number/Examples/6

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Example of Ore Number

$H \left({6}\right) = 2$

where $H \left({n}\right)$ denotes the harmonic mean of the divisors of $n$.


From Harmonic Mean of Divisors in terms of Tau and Sigma:

$H \left({n}\right) = \dfrac {n \, \tau \left({n}\right)} {\sigma \left({n}\right)}$


$\tau \left({n}\right)$ denotes the $\tau$ (tau) function: the number of divisors of $n$
$\sigma \left({n}\right)$ denotes the $\sigma$ (sigma) function: the sum of the divisors of $n$.

\(\displaystyle \tau \left({6}\right)\) \(=\) \(\displaystyle 4\) $\tau$ of $6$
\(\displaystyle \sigma \left({6}\right)\) \(=\) \(\displaystyle 12\) $\sigma$ of $6$
\(\displaystyle \leadsto \ \ \) \(\displaystyle \dfrac {6 \, \tau \left({6}\right)} {\sigma \left({6}\right)}\) \(=\) \(\displaystyle \dfrac {6 \times 4} {12}\)
\(\displaystyle \) \(=\) \(\displaystyle 2\)