# Definition:Aliquot Sum

## Definition

Let $n \in \Z$ be a positive integer.

The aliquot sum $\map s n$ of $n$ is defined as the sum of its aliquot parts.

### Sequence of Aliquot Sums

The sequence of aliquot sums begins:

$\begin{array} {r|r} n & \map s n \\ \hline 1 & 0 \\ 2 & 1 \\ 3 & 1 \\ 4 & 3 \\ 5 & 1 \\ 6 & 6 \\ 7 & 1 \\ 8 & 7 \\ 9 & 4 \\ 10 & 8 \\ 11 & 1 \\ 12 & 16 \\ 13 & 1 \\ 14 & 10 \\ 15 & 9 \\ 16 & 15 \end{array}$

## Also known as

The aliquot sum of a positive integer is also known as the more unwieldy and hence uglier term restricted divisor function.

While the term aliquot part is considered archaic nowadays, it has the advantage of being short and euphonious.

## Linguistic Note

The word aliquot is a Latin word meaning a few, some, or not many.