Definition:Aliquot Sum

From ProofWiki
Jump to: navigation, search

Definition

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

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


Sequence of Aliquot Sums

The sequence of aliquot sums begins:

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

This sequence is A001065 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


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.


Also see


Linguistic Note

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


Sources