This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A063991 #50 Jul 18 2025 14:46:01 %S A063991 114,126,1140,1260,18018,22302,32130,40446,44772,49308,56430,64530, %T A063991 67158,73962,142310,168730,180180,197340,223020,241110,242730,286500, %U A063991 296010,308220,365700,429750,462330,548550,591030,618570,669900,671580,739620,785148,815100,827652,827700,932100 %N A063991 Unitary amicable numbers. %C A063991 From _Amiram Eldar_, Mar 09 2024: (Start) %C A063991 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 A063991 Hagis (1971) calculated the first 19 pairs (the terms below 10^6). %C A063991 Najar (1995) calculated the first 185 pairs (terms whose smaller member is below 10^8). (End) %D A063991 Mariano Garcia, New unitary amicable couples, J. Recreational Math., Vol. 17, No. 1 (1984-5), pp. 32-35. %D A063991 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 A063991 Clifford A. Pickover, The Math Book, Sterling, NY, 2009; see p. 90. %D A063991 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 148. %H A063991 Michel Marcus, <a href="/A063991/b063991.txt">Table of n, a(n) for n = 1..149</a> %H A063991 Peter Hagis, Jr., <a href="http://www.jstor.org/stable/2004356">Unitary amicable numbers</a>, Math. Comp., Vol. 25, No. 116 (1971), pp. 915-918. %H A063991 O. William McClung, <a href="https://web.archive.org/web/2024*/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://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/24-2/letter.pdf">Letter to the Editor</a>, ibid., Vol. 24, No. 2 (1986), p. 106. %H A063991 Rudolph M. Najar, <a href="https://web.archive.org/web/2024*/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 A063991 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 A063991 J. O. M. Pedersen, <a href="http://62.198.248.44/aliquot/knwnu2.htm">Known Unitary Amicable Pairs</a>. %H A063991 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 A063991 J. O. M. Pedersen, <a href="http://62.198.248.44/aliquot/tables.htm">Tables of Aliquot Cycles</a>. %H A063991 J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a>. [Cached copy, pdf file only] %H A063991 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 A063991 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 A063991 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 A063991 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 A063991 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 A063991 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnitaryAmicablePair.html">Unitary Amicable Pair</a>. %o A063991 (PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n; %o A063991 isok1(n) = iferr(f(n) == n, E, 0); %o A063991 isok2(n) = iferr(f(f(n)) == n, E, 0); %o A063991 isok(n) = isok2(n) && !isok1(n); \\ _Michel Marcus_, Sep 29 2018 %Y A063991 Union of A002952 and A002953. %K A063991 nonn %O A063991 1,1 %A A063991 _N. J. A. Sloane_, Sep 18 2001 %E A063991 More terms from _Michel Marcus_, Sep 29 2018