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amicable numbers
A member of a pair (n, m) such that there exist another number σ(n) - n = m and σ(m) - m = n. more

The first 600 amicable numbers :
220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992, 67095, 69615, 71145, 76084, 79750, 87633, 88730, 100485, 122265, 122368, 123152, 124155, 139815, 141664, 142310, 153176, 168730, 171856, 176272, 176336, 180848, 185368, 196724, 202444, 203432, 280540, 308620, 319550, 356408, 365084, 389924, 399592, 430402, 437456, 455344, 469028, 486178, 503056, 514736, 522405, 525915, 600392, 609928, 624184, 635624, 643336, 652664, 667964, 669688, 686072, 691256, 712216, 726104, 783556, 796696, 802725, 863835, 879712, 898216, 901424, 947835, 980984, 998104, 1043096, 1077890, 1099390, 1125765, 1154450, 1156870, 1175265, 1185376, 1189150, 1280565, 1286744, 1292570, 1328470, 1340235, 1358595, 1392368, 1438983, 1464592, 1466150, 1468324, 1483850, 1486845, 1511930, 1598470, 1669910, 1747930, 1749212, 1798875, 1870245, 2062570, 2082464, 2090656, 2236570, 2429030, 2652728, 2723792, 2728726, 2739704, 2802416, 2803580, 2874064, 2928136, 2941672, 2947216, 3077354, 3276856, 3606850, 3716164, 3721544, 3786904, 3805264, 3892670, 4006736, 4238984, 4246130, 4259750, 4300136, 4314616, 4445050, 4482765, 4488910, 4532710, 4604776, 5120595, 5123090, 5147032, 5162744, 5232010, 5357625, 5385310, 5459176, 5495264, 5504110, 5684679, 5726072, 5730615, 5799542, 5812130, 5843048, 5864660, 6088905, 6135962, 6329416, 6369928, 6371384, 6377175, 6680025, 6955216, 6993610, 7158710, 7275532, 7288930, 7418864, 7471508, 7489112, 7489324, 7577350, 7674088, 7677248, 7684672, 7800544, 7850512, 7916696, 8052488, 8221598, 8262136, 8369864, 8493050, 8619765, 8666860, 8754130, 8826070, 9071685, 9199496, 9206925, 9339704, 9363584, 9437056, 9478910, 9491625, 9498555, 9592504, 9627915, 9660950, 9773505, 9892936, 10025290, 10043690, 10254970, 10273670, 10533296, 10572550, 10596368, 10634085, 10638356, 10791795, 10854650, 10893230, 10949704, 10950615, 10992735, 11049730, 11173460, 11199112, 11252648, 11498355, 11545616, 11693290, 11791935, 11905504, 12024045, 12070305, 12101272, 12247504, 12361622, 12397552, 12707704, 13136528, 13212076, 13337336, 13671735, 13813150, 13921528, 13985672, 14084763, 14236136, 14310050, 14311688, 14426230, 14443730, 14654150, 14718712, 15002464, 15334304, 15363832, 15877065, 15882670, 15938055, 16137628, 16150628, 16517768, 16817050, 16871582, 17041010, 17257695, 17308665, 17578785, 17754165, 17844255, 17908064, 18017056, 18056312, 18087818, 18166888, 18194715, 18655744, 19150222, 19154336, 19325698, 19895265, 19985355, 20014808, 20022328, 20308995, 20955645, 21448630, 21457192, 22227075, 22240485, 22249552, 22508145, 22608632, 22823432, 23030090, 23111055, 23358248, 23389695, 23628940, 24472180, 24644925, 25132545, 25233112, 25325528, 25596544, 25640096, 25775368, 25966832, 26090325, 26138475, 26529808, 27428276, 28118032, 28128368, 28608424, 29603576, 30395276, 30724694, 30830696, 31536855, 31652704, 31818952, 32148585, 32174506, 32205616, 32642324, 32685250, 33501825, 34256222, 34352624, 34364912, 34380688, 34538270, 34765731, 34860248, 35095276, 35115795, 35361326, 35373195, 35390008, 35472592, 35997346, 36136575, 36415664, 36939357, 37363095, 37784810, 37848915, 38400512, 38637016, 38663950, 38783992, 38807968, 38938288, 39202605, 39259592, 39944086, 40105845, 40117714, 40678184, 40912232, 41654408, 43096904, 43266285, 43362050, 44139856, 44916944, 45263384, 45663849, 46137016, 46237730, 46271745, 46521405, 46555250, 46715896, 46991890, 48471470, 48639032, 48641584, 48852176, 49125375, 49215166, 50997596, 51737764, 52695376, 52967368, 53011395, 55349570, 55880590, 56055872, 56208368, 56512610, 56598208, 56924192, 58580540, 59497888, 61319902, 61953512, 63560025, 63717615, 64562488, 65003175, 66011985, 66595130, 66854710, 67729064, 67738268, 68891992, 69439576, 70507972, 71015260, 71241830, 71946890, 72958556, 73032872, 74055952, 74386305, 74733604, 74769345, 74824390, 75171808, 75226888, 75866014, 77237792, 78057370, 78088504, 78166448, 78437288, 78447010, 78469528, 79324875, 79732132, 80422335, 80960990, 81265112, 82633005, 82824255, 82977345, 83135650, 84521745, 84591405, 85458596, 85603550, 86158220, 87133365, 87354495, 87998470, 88110536, 88144630, 89477984, 89590995, 90437150, 91996816, 92143456, 93259184, 93837808, 94372450, 95629904, 95791430, 96304845, 96747315, 97041735, 97580944, 97945785, 99188788, 99899792, 102023145, 102358010, 102719740, 102814490, 103034776, 104177619, 104887448, 105016424, 105064552, 107908335, 108734050, 109410345, 110132055, 110960710, 114944072, 115187002, 115259625, 115447424, 115749344, 116251550, 116654896, 116970399, 116983744, 118458830, 118458976, 120115664, 120812175, 121293315, 123757335, 125222330, 125269528, 126671985, 127924335, 129063812, 131118975, 131483835, 131819506, 132692805, 132926625, 133089500, 133178325, 133471275, 133768816, 134312152, 134886465, 136549413, 136770075, 137424188, 138605350, 138690045, 139009990, 139057448, 140207067, 140744835, 140815384, 141213584, 141993412, 144788020, 145040288, 146648612, 147313850, 147366765, 147382335, 148077644, 148532625, 149364256, 153015550, 154190750, 155578180, 155709416, 155711205, 155797390, 156226856, 156322490, 157151410, 159017308, 160128436, 161088158, 162936904, 163634510, 164733752, 165181144, 165195890, 165323696, 165742395, 166212808, 166562685, 166679096, 166706530, 166737550, 167155024, 168392450, 168930032, 169000448, 169335790, 169652512, 169884784, 170566690, 172271385, 172610492, 173269088, 173499952, 173843216, 175032884, 175826716, 176374564, 176632390, 177997352, 179029010, 179904784, 180038452, 181088985, 182028483, 182108128, 182618810, 182622405, 182702024, 183408615, 184694055, 184713976, 186088988, 186753688, 186878110, 188953970, 189406984, 190055385, 190888155, 190889986, 193486028, 194594085, 195857415, 196214265, 196323170.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 77977 values, from 220 to 99999610625475).

n\r 0  1 
24758630391 2 
3303912380823778 3 
430996151891659015202 4 
5386429785983298689850 5 
6002377830391238080 6 
71882796409866101471002598099663 7 
8233997552830676427597763782847560 8 
92398080137824309979367937331278598017 9 
10131751251862011308519254678534121287381331 10 
11201445780564758455720581858875881579756345824

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.