Ore Number/Examples/1638

Example of Ore Number

 * $\map H {1638} = 9$

where $\map H n$ denotes the harmonic mean of the divisors of $n$.

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

where:
 * $\map \tau n$ denotes the divisor counting (tau) function: the number of divisors of $n$
 * $\map \sigma n$ denotes the $\sigma$ (sigma) function: the sum of the divisors of $n$.