Unitary Amicable Pair

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

$$\sigma^*(m)=\sigma^*(n)=m+n,$$

where $\sigma^*(n)$ is the sum of Unitary Divisors. Hagis (1971) and García (1987) give 82 such pairs. The first few are (114, 126), (1140, 1260), (18018, 22302), (32130, 40446), ... (Sloane's A002952 and A002953).

References

García, M. ``New Unitary Amicable Couples.'' J. Recr. Math. 19, 12-14, 1987.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 57, 1994.

Hagis, P. ``Relatively Prime Amicable Numbers of Opposite Parity.'' Math. Comput. 25, 915-918, 1971.

Sloane, N. J. A. Sequences A002952/M5372 and A002953/M5389 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.