A unitary amicable pair is a pair of distinct positive integers
where 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).
In January 2004, Y. Kohmoto reported a unitary amicable pair in which each member has 317 digits, a record at the time (Peterson 2004).
Kohmoto calls a unitary amicable pair whose members are squareful
a proper unitary amicable pair.
See also 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. Hagis, P., Jr. "Unitary Amicable Numbers." Math. Comput. 25 ,
915-918, 1971. https://doi.org/10.1090/S0025-5718-1971-0299551-2 . Kohmoto,
Y. "Aliquot Cycles and Generalizations." http://boat.zero.ad.jp/~zbi74583/aliquot.htm . Kohmoto,
Y. "Record of Unitary Amicable Pair." https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0401&L=nmbrthry&F=&S=&P=2345 . Pedersen,
J. M. "Known Unitary Amicable Pairs." https://web.archive.org/web/20020607013320/http://amicable.homepage.dk:80/knwnunap.htm . Peterson,
I. "Amicable Pairs, Divisors, and a New Record." Jan. 30, 2004. https://www.sciencenews.org/article/amicable-pairs-divisors-and-new-record . 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 https://mathworld.wolfram.com/UnitaryAmicablePair.html
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and 
such that
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).
