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→Example: example with sigma_{-1} |
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s(12) & = 1^1 + 2^1 + 3^1 + 4^1 + 6^1 \\
& = 1 + 2 + 3 + 4 + 6 = 16.
\end{align}
</math>
σ<sub>-1</sub>(''n'') is sometimes called the [[abundancy index]] of ''n'', and we have:
: <math>
\begin{align}
\sigma_{-1}(12) & = 1^{-1} + 2^{-1} + 3^{-1} + 4^{-1} + 6^{-1} + 12^{-1} \\
& = \tfrac11 + \tfrac12 + \tfrac13 + \tfrac14 + \tfrac16 + \tfrac1{12} \\
& = \tfrac{12}{12} + \tfrac6{12} + \tfrac4{12} + \tfrac3{12} + \tfrac2{12} + \tfrac1{12} \\
& = \tfrac{12 + 6 + 4 + 3 + 2 + 1}{12} = \tfrac{28}{12} = \tfrac73 = \tfrac{\sigma_1(12)}{12}
\end{align}
</math>
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