Category:Definitions/Aliquot Sequences

This category contains definitions related to Aliquot Sequences.
Related results can be found in Category:Aliquot Sequences.

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.