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Unitary Amicable Pair

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A pair of numbers m and n such that

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

where sigma^*(n) 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.

See also

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."

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Unitary Amicable Pair

Cite this as:

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

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