%I #42 Mar 09 2024 05:58:22
%S 114,126,1140,1260,18018,22302,32130,40446,44772,49308,56430,64530,
%T 67158,73962,142310,168730,180180,197340,223020,241110,242730,286500,
%U 296010,308220,365700,429750,462330,548550,591030,618570,669900,671580,739620,785148,815100,827652,827700,932100
%N Unitary amicable numbers.
%C From _Amiram Eldar_, Mar 09 2024: (Start)
%C The concept of unitary amicable numbers was introduced by Wall (1970), who proved that both members of a pair are either odd or even, and found 610 pairs (only 592 were correct, as found by te Riele, 1978).
%C Hagis (1971) calculated the first 19 pairs (the terms below 10^6).
%C Najar (1995) calculated the first 185 pairs (terms whose smaller member is below 10^8). (End)
%D Mariano Garcia, New unitary amicable couples, J. Recreational Math., Vol. 17, No. 1 (1984-5), pp. 32-35.
%D M. Lal, G. Tiller, and T. Summers, Unitary sociable numbers, Proceedings of the Second Manitoba Conference on Numerical Mathematics, Congressus Numerantium No. 7, 1972, pp. 211-216.
%D Clifford A. Pickover, The Math Book, Sterling, NY, 2009; see p. 90.
%H Michel Marcus, <a href="/A063991/b063991.txt">Table of n, a(n) for n = 1..149</a>
%H Peter Hagis, Jr., <a href="http://www.jstor.org/stable/2004356">Unitary amicable numbers, Math. Comp., Vol. 25, No. 116 (1971), pp. 915-918.
%H O. William McClung, <a href="https://www.fq.math.ca/Scanned/23-2/mcclung.pdf">Generators of Unitary Amicable Numbers</a>, Fibonacci Quarterly, Vol. 23, No. 2 (1985), pp. 158-164; <a href="https://www.fq.math.ca/Scanned/24-2/letter.pdf">Letter to the Editor</a>, ibid., Vol. 24, No. 2 (1986), p. 106.
%H Rudolph M. Najar, <a href="https://www.fq.math.ca/Scanned/27-2/najar.pdf">Operations on Generators of Unitary Amicable Pairs</a>, Fibonacci Quarterly, Vol. 27, No. 2 (1989), pp. 144-152.
%H Rudolph M. Najar, <a href="https://doi.org/10.1155/S0161171295000512">The Unitary Amicable Pairs To 10^8</a>, International Journal of Mathematics and Mathematical Sciences, Volume 18, No. 2 (1995), pp. 405-410, Article ID 396507, 6 pages.
%H J. O. M. Pedersen, <a href="http://62.198.248.44/aliquot/knwnu2.htm">Known Unitary Amicable Pairs</a>.
%H J. O. M. Pedersen, <a href="https://web.archive.org/web/20070617233144/http://amicable.homepage.dk/knwnu2.htm">Known Unitary Amicable Pairs</a>. [Via Wayback Machine]
%H J. O. M. Pedersen, <a href="http://62.198.248.44/aliquot/tables.htm">Tables of Aliquot Cycles</a>.
%H J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a>. [Cached copy, pdf file only]
%H Ivars Peterson, <a href="https://web.archive.org/web/20130126192043/http://www.maa.org/mathland/mathtrek_02_02_04.html">Amicable Pairs, Divisors and a New Record</a>, February 2, 2004.
%H Herman J. J. te Riele, <a href="https://ir.cwi.nl/pub/9068">Further Results on Unitary Aliquot Sequences</a>, Report NW 2/78, Math. Centre, Amsterdam, 2nd ed., Jan. 1978.
%H Herman J. J. te Riele, <a href="https://ir.cwi.nl/pub/13093/">A theoretical and computational study of generalized aliquot sequences</a>, Mathematisch Centrum, Amsterdam, 1976.
%H Herman J. J. te Riele, <a href="https://ir.cwi.nl/pub/9137">Unitary Aliquot Sequences</a>, MR 139/72, Mathematisch Centrum, Amsterdam, 1972.
%H Charles Robert Wall, <a href="https://trace.tennessee.edu/utk_graddiss/8570/">Topics related to the sum of unitary divisors of an integer</a>, Ph.D. diss., University of Tennessee, 1970.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitaryAmicablePair.html">Unitary Amicable Pair</a>.
%o (PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;
%o isok1(n) = iferr(f(n) == n, E, 0);
%o isok2(n) = iferr(f(f(n)) == n, E, 0);
%o isok(n) = isok2(n) && !isok1(n); \\ _Michel Marcus_, Sep 29 2018
%Y Union of A002952 and A002953.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Sep 18 2001
%E More terms from _Michel Marcus_, Sep 29 2018