Quasiamicable Pair

Let $\sigma(m)$ be the Divisor Function of $m$. Then two numbers $m$ and $n$ are a quasiamicable pair if

$$\sigma(m)=\sigma(n)=m+n+1.$$

The first few are (48, 75), (140, 195), (1050, 1575), (1648, 1925), ... (Sloane's A005276). Quasiamicable numbers are sometimes called Betrothed Numbers or Reduced Amicable Pairs.

See also Amicable Pair

References

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

Guy, R. K. ``Quasi-Amicable or Betrothed Numbers.'' §B5 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 59-60, 1994.

Hagis, P. and Lord, G. ``Quasi-Amicable Numbers.'' Math. Comput. 31, 608-611, 1977.

Sloane, N. J. A. Sequence A005276/M5291 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.