Ore Number/Examples/496
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Example of Ore Number
- $\map H {496} = 5$
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 count function: the number of divisors of $n$
- $\map {\sigma_1} n$ denotes the divisor sum function: the sum of the divisors of $n$.
\(\ds \map {\sigma_0} {496}\) | \(=\) | \(\ds 10\) | $\sigma_0$ of $496$ | |||||||||||
\(\ds \map {\sigma_1} {496}\) | \(=\) | \(\ds 992\) | $\sigma_1$ of $496$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \dfrac {496 \, \map {\sigma_0} {496} } {\map {\sigma_1} {496} }\) | \(=\) | \(\ds \dfrac {496 \times 10} {992}\) | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {\paren {2^4 \times 31} \times \paren {2 \times 5} } {\paren {2^5 \times 31} }\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 5\) |
$\blacksquare$