Definition:Quasiamicable Numbers/Definition 2

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:

$\map {\sigma_1} m = \map {\sigma_1} n = m + n + 1$

where $\sigma_1$ denotes the divisor sum function.

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

• Equivalence of Definitions of Quasiamicable Numbers

Sources

• Weisstein, Eric W. "Quasiamicable Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/QuasiamicablePair.html