Editing Divisor function (section)

==Example==
For example, ''σ''<sub>0</sub>(12) is the number of the divisors of 12:

: <math>
\begin{align}
\sigma_0(12) & = 1^0 + 2^0 + 3^0 + 4^0 + 6^0 + 12^0 \\
& = 1 + 1 + 1 + 1 + 1 + 1 = 6,
\end{align}
</math>

while ''σ''<sub>1</sub>(12) is the sum of all the divisors:

: <math>
\begin{align}
\sigma_1(12) & = 1^1 + 2^1 + 3^1 + 4^1 + 6^1 + 12^1 \\
& = 1 + 2 + 3 + 4 + 6 + 12 = 28,
\end{align}
</math>

and the aliquot sum s(12) of proper divisors is:

: <math>
\begin{align}
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} \\[6pt]
& = \tfrac11 + \tfrac12 + \tfrac13 + \tfrac14 + \tfrac16 + \tfrac1{12} \\[6pt]
& = \tfrac{12}{12} + \tfrac6{12} + \tfrac4{12} + \tfrac3{12} + \tfrac2{12} + \tfrac1{12} \\[6pt]
& = \tfrac{12 + 6 + 4 + 3 + 2 + 1}{12} = \tfrac{28}{12} = \tfrac73 = \tfrac{\sigma_1(12)}{12}
\end{align}
</math>