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 A259933 Amicable pairs (x < y) ordered by nondecreasing sum (x + y) and then by increasing x. 15
 220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 66928, 66992, 67095, 71145, 63020, 76084, 69615, 87633, 79750, 88730, 100485, 124155, 122368, 123152, 122265, 139815, 141664, 153176, 142310, 168730, 171856, 176336, 176272, 180848, 185368, 203432, 196724, 202444, 280540, 365084, 308620, 389924 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. By definition a property of the amicable pair (x, y) is that x + y = sigma(x) = sigma(y). The amicable pairs (x < y) are adjacent to each other in the list. Also A260086 and A260087 interleaved. Another version (A259180) lists the amicable pairs (x < y) ordered by increasing x. Amicable numbers A063990 are the terms of this sequence in increasing order. First differs from both A063990 and A259180 at a(17). LINKS Table of n, a(n) for n=1..48. Laszlo Hars, Performance compared to mathematica Julia-users (2014) Khelleos, Amicable numbers, CyberForum.ru (2011) OEIS Wiki, Amicable numbers (This page needs work) Wikipédia, Barátságos számok (contains a mistake: A063990 should be replaced with A259933) FORMULA a(2n-1) + a(2n) = A000203(a(2n-1)) = A000203(a(2n)) = A259953(n). EXAMPLE ----------------------------------- Amicable pair Sum x y x + y ----------------------------------- n A260086 A260087 A259953 ----------------------------------- 1 220 284 504 2 1184 1210 2394 3 2620 2924 5544 4 5020 5564 10584 5 6232 6368 12600 6 10744 10856 21600 7 12285 14595 26880 8 17296 18416 35712 9 66928 66992 133920 10 67095 71145 138240 11 63020 76084 139104 12 69615 87633 157248 ... ... ... ... 32 609928 686072 1296000 33 643336 652664 1296000 ... 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. 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. CROSSREFS Cf. A000203, A063990, A259180, A259953, A260086, A260087. Sequence in context: A255215 A063990 A259180 * A273259 A262624 A262622 Adjacent sequences: A259930 A259931 A259932 * A259934 A259935 A259936 KEYWORD nonn AUTHOR Omar E. Pol, Jul 09 2015 STATUS approved

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)