Definition:Quasiamicable Numbers/Definition 1
Jump to navigation
Jump to search
Definition
Let $m \in \Z_{>0}$ and $n \in \Z_{>0}$ be (strictly) positive integers.
$m$ and $n$ are quasiamicable numbers if and only if:
- the sum of the proper divisors of $m$ is equal to $n$
and:
- the sum of the proper divisors of $n$ is equal to $m$.
Sequence
The sequence of quasiamicable pairs begins:
- $\tuple {48, 75}, \tuple {140, 195}, \tuple {1050, 1925}, \tuple {1575, 1648} \ldots$
Examples
$48$ and $75$
$48$ and $75$ form a quasiamicable pair.
$140$ and $195$
$140$ and $195$ form a quasiamicable pair.
$1050$ and $1925$
$1050$ and $1925$ form a quasiamicable pair.
$1575$ and $1648$
$1575$ and $1648$ form a quasiamicable pair.
Also see
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $48$