cp's OEIS Frontend

A002046 Larger of amicable pair.

%I A002046 M5435 N2363 #97 Jul 02 2025 11:34:45
%S A002046 284,1210,2924,5564,6368,10856,14595,18416,76084,66992,71145,87633,
%T A002046 88730,124155,139815,123152,153176,168730,176336,180848,203432,202444,
%U A002046 365084,389924,430402,399592,455344,486178,514736,525915,669688,686072
%N A002046 Larger of amicable pair.
%C A002046 The elements 76084, 123152, etc. are intentionally out of numerical order so that a(n) and A002025(n) form amicable pairs. - _Michael B. Porter_, Apr 17 2010
%C A002046 All terms are deficient (A005100). - _Michel Marcus_, Mar 10 2013
%C A002046 For the related amicable pairs see A259180. - _Omar E. Pol_, Jul 15 2015
%D A002046 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002046 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002046 For additional references see A002025.
%H A002046 T. D. Noe and Sergei Chernykh, <a href="/A002046/b002046.txt">Table of n, a(n) for n = 1..415523</a> [All terms such that the smaller number A002025(n) is < 10^17. Terms 39375 through 415523 were computed by Sergei Chernykh]
%H A002046 J. Bell, <a href="http://arXiv.org/abs/math.NT/0409196">A translation of Leonhard Euler's "On amicable numbers"</a>, arXiv:math/0409196 [math.HO], 2004-2009.
%H A002046 S. Chernykh, <a href="http://sech.me/ap/">Amicable pairs list</a>
%H A002046 E. B. Escott, <a href="/A002025/a002025.pdf">Amicable numbers</a>, Scripta Mathematica, 12 (1946), 61-72 [Annotated scanned copy]
%H A002046 M. Garcia, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL4/GARCIA/millionc.html">A Million New Amicable Pairs</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.6.
%H A002046 S. S. Gupta, <a href="http://www.shyamsundergupta.com/amicable.htm">Amicable Numbers</a>
%H A002046 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math09/ami02.htm">First 236 amicable pairs</a>
%H A002046 David Moews, <a href="http://djm.cc/amicable.html">Perfect, amicable and sociable numbers</a>
%H A002046 Passawan Noppakaew and Prapanpong Pongsriiam, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Pongsriiam/pong43.html">Product of Some Polynomials and Arithmetic Functions</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.9.1.
%H A002046 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/knwnap.htm">Known Amicable Pairs</a> [Broken link]
%H A002046 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Broken link]
%H A002046 J. O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Via Internet Archive Wayback-Machine]
%H A002046 J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a> [Cached copy, pdf file only]
%H A002046 T. Trotter, Jr., <a href="https://www.trottermath.net/numthry/amicable.html">Amicable Numbers</a>
%H A002046 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AmicablePair.html">Amicable Pair</a>
%F A002046 a(n) = A259180(2n) = A180164(n) - A259180(2n-1) = A180164(n) - A002025(n). - _Omar E. Pol_, Jul 15 2015
%p A002046 f:= proc(t) uses numtheory; local s;
%p A002046   s:= sigma(t) - t; s > t and sigma(s) - s = t
%p A002046 end proc;
%p A002046 Am1:= select(f,[$1..10^6]);
%p A002046 map(numtheory:-sigma,Am1); # _Robert Israel_, Jul 16 2015
%t A002046 amicableQ[n_] := With[{s = DivisorSigma[1, n] - n}, r = n != s && n == DivisorSigma[1, s] - s; If[r, mate[n] = s; True, False]]; mate /@ Select[ Range[lim], amicableQ[#] && # < mate[#] &] (* _Jean-François Alcover_, Sep 20 2011 *)
%t A002046 Table[DivisorSigma[1, A002025[n]] - A002025[n], {n, 50}] (* _T. D. Noe_, Sep 20 2011 *)
%o A002046 (PARI) aliquot(n)=sigma(n)-n
%o A002046 isA002046(n)={if (n>1, local(a);a=aliquot(n);a<n && aliquot(a)==n)} \\ _Michael B. Porter_, Apr 17 2010
%Y A002046 Cf. A002025, A063990, A180164, A259180.
%K A002046 nonn,nice
%O A002046 1,1
%A A002046 _N. J. A. Sloane_
%E A002046 More terms from Larry Reeves (larryr(AT)acm.org), Oct 25 2000