Augmented Amicable Pairs

abohlke812 13 Oct 2008 22:52

So I was researching amicable pairs, and I found this definition of augmented amicable pairs:

A pair of numbers m and n such that

(1)\begin{align} \sigma (m) = \sigma (n) = m + n - 1 \end{align}

It said that only 11 pairs of augmented amicable pairs have been found.

I was wondering if there were any other types of augmented pairs, maybe such that

\begin{align} \sigma (m) = \sigma (n) = m + n + 1 or =m + n - 2 \end{align}