Divisor Function - Example

Example

For example, σ0(12) is the number of the divisors of 12:

\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}

while σ1(12) is the sum of all the divisors:

\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}

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

\begin{align} s(12) & = 1^1 + 2^1 + 3^1 + 4^1 + 6^1 \\ & = 1 + 2 + 3 + 4 + 6 = 16. \end{align}

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