Augmented Amicable Pair

A Pair of numbers $m$ and $n$ such that

$$\sigma(m)=\sigma(n)=m+n-1,$$

where $\sigma(m)$ is the Divisor Function. Beck and Najar (1977) found 11 augmented amicable pairs.

See also Amicable Pair, Divisor Function, Quasiamicable Pair

References

Beck, W. E. and Najar, R. M. ``More Reduced Amicable Pairs.'' Fib. Quart. 15, 331-332, 1977.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 59, 1994.