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 Divisor Count and Divisor Sum:
 * $\map H n = \dfrac {n \, \map {\sigma_0} n} {\map {\sigma_1} n}$

where:
 * $\map {\sigma_0} n$ denotes the divisor counting function: the number of divisors of $n$
 * $\map {\sigma_1} n$ denotes the divisor sum function: the sum of the divisors of $n$.