Category:Definitions/Amicable Pairs

This category contains definitions related to Amicable Pairs.
Related results can be found in Category:Amicable Pairs.

Definition 1

$m$ and $n$ are an amicable pair if and only if:

the aliquot sum of $m$ is equal to $n$

and:

the aliquot sum of $n$ is equal to $m$.

Definition 2

$m$ and $n$ are an amicable pair if and only if:

$\map {\sigma_1} m = \map {\sigma_1} n = m + n$

where $\sigma_1$ denotes the divisor sum function.

Definition 3

$m$ and $n$ are an amicable pair if and only if they form a sociable chain of order $2$.