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Date: 1-2-2021
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Date: 3-2-2020
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Date: 17-11-2020
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A pair of numbers and
such that
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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.
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." https://boat.zero.ad.jp/~zbi74583/aliquot.htm.
Kohmoto, Y. "Record of Unitary Amicable Pair." https://listserv.nodak.edu/scripts/wa.exe?A2=ind0401&L=nmbrthry&F=&S=&P=2345.
Pedersen, J. M. "Known Unitary Amicable Pairs." https://amicable.homepage.dk/knwnunap.htm.
Peterson, I. "Amicable Pairs, Divisors, and a New Record." Jan. 31, 2004. https://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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