Ore Number/Examples/140

Example of Ore Number

 * $H \left({140}\right) = 5$

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

Proof
From Harmonic Mean of Divisors in terms of Tau and Sigma:
 * $H \left({n}\right) = \dfrac {n \, \tau \left({n}\right)} {\sigma \left({n}\right)}$

where:
 * $\tau \left({n}\right)$ 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 $n$.