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 A259933 #65 Jul 15 2015 18:02:24 %S A259933 220,284,1184,1210,2620,2924,5020,5564,6232,6368,10744,10856,12285, %T A259933 14595,17296,18416,66928,66992,67095,71145,63020,76084,69615,87633, %U A259933 79750,88730,100485,124155,122368,123152,122265,139815,141664,153176,142310,168730,171856,176336,176272,180848,185368,203432,196724,202444,280540,365084,308620,389924 %N A259933 Amicable pairs (x < y) ordered by nondecreasing sum (x + y) and then by increasing x. %C A259933 A pair of numbers x and y is called amicable if the sum of the proper divisors (or aliquot parts) of either one is equal to the other. %C A259933 By definition a property of the amicable pair (x, y) is that x + y = sigma(x) = sigma(y). %C A259933 The amicable pairs (x < y) are adjacent to each other in the list. %C A259933 Also A260086 and A260087 interleaved. %C A259933 Another version (A259180) lists the amicable pairs (x < y) ordered by increasing x. %C A259933 Amicable numbers A063990 are the terms of this sequence in increasing order. %C A259933 First differs from both A063990 and A259180 at a(17). %H A259933 Laszlo Hars, <a href="https://www.mail-archive.com/julia-users@googlegroups.com/msg04022.html">Performance compared to mathematica</a> Julia-users (2014) %H A259933 Khelleos, <a href="http://www.cyberforum.ru/lisp/thread386611.html">Amicable numbers</a>, CyberForum.ru (2011) %H A259933 OEIS Wiki, <a href="https://oeis.org/wiki/Amicable_numbers">Amicable numbers</a> (This page needs work) %H A259933 Wikipédia, <a href="https://hu.wikipedia.org/wiki/Barátságos_számok">Barátságos számok</a> (contains a mistake: A063990 should be replaced with A259933) %F A259933 a(2n-1) + a(2n) = A000203(a(2n-1)) = A000203(a(2n)) = A259953(n). %e A259933 ----------------------------------- %e A259933 Amicable pair Sum %e A259933 x y x + y %e A259933 ----------------------------------- %e A259933 n A260086 A260087 A259953 %e A259933 ----------------------------------- %e A259933 1 220 284 504 %e A259933 2 1184 1210 2394 %e A259933 3 2620 2924 5544 %e A259933 4 5020 5564 10584 %e A259933 5 6232 6368 12600 %e A259933 6 10744 10856 21600 %e A259933 7 12285 14595 26880 %e A259933 8 17296 18416 35712 %e A259933 9 66928 66992 133920 %e A259933 10 67095 71145 138240 %e A259933 11 63020 76084 139104 %e A259933 12 69615 87633 157248 %e A259933 ... ... ... ... %e A259933 32 609928 686072 1296000 %e A259933 33 643336 652664 1296000 %e A259933 ... %e A259933 The sum of the proper divisors (or aliquot parts) of 220 is 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284. On the other hand the sum of the proper divisors (or aliquot parts) of 284 is 1 + 2 + 4 + 71 + 142 = 220. Note that 220 + 284 = sigma(220) = sigma(284) = 504. The sum 220 + 284 = 504 is the smallest sum of an amicable pair, so a(1) = 220 and a(2) = 284. %e A259933 Note that some pairs (x, y) share the same sum (x + y), for example: (609928 + 686072) = (643336 + 652664) = sigma(609928) = sigma(686072) = sigma(643336) = sigma(652664) = 1296000, thus in the list first appears the pair (609928, 686072) and then (643336, 652664) because 609928 < 643336. %Y A259933 Cf. A000203, A063990, A259180, A259953, A260086, A260087. %K A259933 nonn %O A259933 1,1 %A A259933 _Omar E. Pol_, Jul 09 2015