\begin{definition}[Definition:Aliquot Sequence]
Let $m$ be a positive integer.
Let $\map s m$ be the aliquot sum of $m$.
Define the sequence $\sequence {a_k}$ recursively as:
:$a_{k + 1} = \begin{cases} m & : k = 0 \\ \map s {a_k} & : k > 0 \end{cases}$
The sequence $\sequence {a_k}$ is known as an '''aliquot sequence'''.
\end{definition}