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# Unitary Amicable Pair

A pair of numbers and such that

where is the unitary divisor function. Hagis (1971) and García (1987) give 82 such pairs. The first few are (114, 126), (1140, 1260), (18018, 22302), (32130, 40446), ... (OEIS A002952 and A002953; Pedersen).

On Jan. 30, 2004, Y. Kohmoto discovered the largest known unitary amicable pair, where each member has 317 digits.

Kohmoto calls a unitary amicable pair whose members are squareful a proper unitary amicable pair.

Amicable Pair, Super Unitary Amicable Pair, Unitary Aliquot Sequence, Unitary Divisor, Unitary Divisor Function

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## 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.Kohmoto, Y. "Aliquot Cycles and Generalizations." http://boat.zero.ad.jp/~zbi74583/aliquot.htm.Kohmoto, Y. "Record of Unitary Amicable Pair." http://listserv.nodak.edu/scripts/wa.exe?A2=ind0401&L=nmbrthry&F=&S=&P=2345.Pedersen, J. M. "Known Unitary Amicable Pairs." http://amicable.homepage.dk/knwnunap.htm.Peterson, I. "Amicable Pairs, Divisors, and a New Record." Jan. 31, 2004. http://www.sciencenews.org/20040131/mathtrek.asp.Sloane, N. J. A. Sequences A002952/M5372 and A002953/M5389 in "The On-Line Encyclopedia of Integer Sequences."

## Referenced on Wolfram|Alpha

Unitary Amicable Pair

## Cite this as:

Weisstein, Eric W. "Unitary Amicable Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UnitaryAmicablePair.html