婚对数——有趣的自然数及其性质（三）

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婚对数  准友好数
https://www.numbersaplenty.com/set/betrothed_number/

betrothed pairs  婚对数（订婚对）
Two numbers (m,n) form a betrothed pair if the sum of nontrivial divisors of one number equals the other, i.e., if σ(n)-n-1=m and σ(m)-m-1=n.
如果一个数n的非平凡约数之和减n再减1等于另一个数m，另一个数m的非平凡约数之和减m再减1等于第一个数n，即σ(n)-n-1=m且σ(m)-m-1=n，则这两个数(m,n)形成一对订婚对。
例48的因子有1,2,3,4,6,8,12,16,24,48，σ(48)=1+2+3+4+6+8+12+16+24+48=124，σ(48)=48-1=75；75的因子有1,3,5,15,25,75，σ(75)=1+3+5+15+25+75=124，σ(75)=75-1=48；48和75是一对婚对数（准友好数）。

The first numbers which belong to a betrothed pair are
属于订婚对的最初的数字是
( 48 , 75 ), ( 140 , 195 ), ( 1050 , 1925 ), ( 1575 , 1648 ), ( 2024 , 2295 ), ( 5775 , 6128 ), ( 8892 , 16587 ) ), ( 9504 , 20735 ), ( 62744 , 75495 ), ( 186615 , 206504 )更多条款

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The first 600 betrothed numbers :
48, 75, 140, 195, 1050, 1575, 1648, 1925, 2024, 2295, 5775, 6128, 8892, 9504, 16587, 20735, 62744, 75495, 186615, 196664, 199760, 206504, 219975, 266000, 309135, 312620, 507759, 526575, 544784, 549219, 573560, 587460, 817479, 1000824, 1057595, 1081184, 1139144, 1140020, 1159095, 1173704, 1208504, 1233056, 1236536, 1279950, 1331967, 1341495, 1348935, 1459143, 1524831, 1763019, 1902215, 1921185, 2036420, 2102750, 2140215, 2142945, 2171240, 2198504, 2226014, 2312024, 2421704, 2576945, 2580864, 2681019, 2958500, 3010215, 3123735, 3220119, 3676491, 4012184, 4282215, 4311024, 5088650, 5416280, 5644415, 6081680, 6446325, 6618080, 7460004, 7509159, 7875450, 7890575, 8713880, 8829792, 9247095, 9345903, 10106504, 10925915, 12146750, 12251679, 12500865, 12900734, 13693959, 13922100, 14371104, 16247745, 16381925, 18845855, 22013334, 22559060, 23379224, 23939685, 26409320, 26502315, 26525415, 27735704, 27862695, 28206815, 28219664, 31213899, 31356314, 32014575, 33299000, 34093304, 37291625, 37324584, 40818855, 41137620, 41950359, 42125144, 43321095, 49217084, 52026920, 52389315, 52601360, 58354119, 61423340, 62252000, 64045904, 66086504, 66275384, 68337324, 69090615, 70112175, 72917000, 76011992, 77723360, 80870615, 84854315, 85141719, 87689415, 87802407, 88567059, 89446860, 93423519, 93993830, 94713300, 94970204, 96751395, 97389039, 97797104, 99735705, 100256480, 101366342, 101589320, 102019644, 105993657, 106004024, 106524264, 114332175, 114859884, 115780599, 116329136, 116481464, 116540304, 117106064, 117869940, 128707425, 128825415, 129081735, 130016744, 130304888, 133592175, 134064584, 139829624, 140687415, 141649235, 142287992, 145810719, 147041504, 150157215, 152340944, 153582624, 154043505, 154885920, 157470404, 157906430, 158948000, 160797560, 161733825, 161888544, 162156995, 164340224, 164799635, 165416048, 165507975, 166335255, 168102044, 168669879, 170262560, 171553635, 172622505, 173431335, 174080799, 175742294, 178415048, 183651663, 184191111, 189208575, 191800455, 193773447, 195318500, 197570264, 197845235, 198727544, 198978584, 199563195, 201006414, 204064175, 205556894, 207351704, 208548624, 210391694, 210533904, 214559631, 215676320, 226351671, 226964240, 227323250, 227437280, 230092730, 231472535, 233348655, 237110120, 237316959, 237435495, 240536075, 242854884, 248611815, 252734468, 260310375, 261335025, 261412235, 262754384, 265664175, 268315515, 269436699, 271842885, 274313564, 281885919, 285695190, 290057624, 293057960, 296092784, 300215895, 308040104, 308322399, 311172785, 313001199, 313472880, 316305549, 322435295, 335622279, 338626574, 341660220, 344163140, 348865935, 350145775, 350646435, 353587304, 354818060, 367762395, 374770655, 376157079, 379137590, 380747960, 390655395, 396897759, 400950459, 401836344, 407482460, 417152295, 419396439, 420556695, 421077215, 428870144, 436621604, 442147544, 443390409, 447538784, 449036315, 460824848, 478571775, 479527244, 486142620, 499295384, 506589020, 508826439, 516860015, 530004915, 548544744, 559939625, 579753384, 592455015, 597781820, 599291000, 627398240, 638390511, 645632204, 653318420, 654929715, 659384739, 662138295, 665749784, 676362435, 713342504, 721644104, 724235784, 726558860, 728192415, 734590850, 740532716, 754727336, 783839264, 787047488, 794572779, 794589635, 816390819, 817931828, 820888964, 844622295, 851088615, 856444875, 882424179, 888514263, 902555024, 921943035, 926979200, 932552445, 933562055, 949977644, 951044031, 953056175, 959131635, 980389395, 987558704, 987827555, 991087064, 1010000396, 1023736328, 1033002620, 1033763744, 1035813500, 1051937271, 1059627800, 1098115136, 1101593295, 1106039775, 1123418384, 1131760935, 1141074704, 1145890340, 1151128055, 1154706804, 1155794079, 1174809285, 1194885075, 1199626119, 1212941114, 1217353016, 1224278615, 1226825000, 1252992015, 1261742180, 1265855255, 1283921184, 1298344383, 1307247711, 1312252784, 1343056365, 1351707560, 1366942575, 1370080899, 1378574624, 1406830964, 1450207250, 1467581780, 1473700515, 1488607820, 1489939143, 1506753884, 1516137615, 1517220584, 1526208579, 1526672420, 1531953080, 1532741210, 1532917659, 1547906100, 1559119688, 1560890925, 1648746735, 1654350615, 1679061285, 1682066420, 1699088859, 1704525074, 1727172314, 1741044500, 1742984919, 1764267764, 1778869064, 1782222399, 1783523511, 1795408875, 1816402964, 1840746500, 1858726155, 1862919435, 1883876000, 1903187979, 1906051160, 1910285792, 1939995596, 1982390795, 1992599648, 1996209375, 2006332664, 2012227784, 2020337564, 2050561604, 2052672999, 2082593240, 2085372512, 2105199135, 2132355440, 2139198039, 2144382135, 2160543104, 2169354564, 2193824940, 2234106495, 2239676220, 2258708859, 2267171640, 2293334424, 2296563555, 2313337515, 2325991220, 2327248287, 2343404979, 2350626615, 2355309824, 2359000280, 2361854565, 2367009189, 2411826759, 2413813688, 2418204404, 2423454264, 2436393924, 2441496464, 2458574180, 2490395120, 2498946345, 2510904284, 2540165144, 2541717555, 2573840619, 2576707335, 2589127190, 2595146084, 2596144160, 2604140475, 2641212315, 2652982304, 2670130904, 2689435034, 2705286500, 2716915824, 2731700565, 2732097951, 2746338504, 2758505540, 2772801024, 2776954719, 2784075434, 2806455200, 2819077155, 2837602520, 2838165615, 2849128359, 2887857819, 2898322575, 2920453095, 2921793224, 2931650631, 2957731824, 3014994744, 3031422944, 3039432200, 3045615579, 3085130664, 3105475295, 3119339775, 3155451915, 3157070504, 3163223580, 3181556664, 3199177995, 3215269364, 3269502495, 3285728264, 3298072995, 3301952895, 3373298144, 3373643979, 3419884580, 3424407504, 3442577624, 3450876624, 3495040604, 3515685984, 3552265695, 3556889895, 3585589215, 3667278375, 3667561695, 3698827335, 3705257675, 3712611104, 3715037920, 3731353430, 3735363879, 3762043760, 3770681655, 3824655464, 3831852284, 3856140890, 3947516859, 3955132335, 3958280535, 3971454759, 3985532264, 3991840515, 3995575155, 4013193275, 4035324755, 4092444884, 4095184040, 4106225144, 4109899464, 4121667615, 4126705730, 4128822368, 4129427384, 4133786964, 4165376480, 4184346704, 4197999399, 4236950375, 4239746469, 4253975684, 4264348088, 4332612585, 4333216635, 4364776125, 4372365500, 4382760704, 4388870115, 4415176844, 4438526780, 4479663936, 4482524150, 4516899849, 4523120315, 4537964535, 4587544604, 4604412384, 4618069599, 4643378844, 4666112264, 4668784835, 4677638955, 4696878944, 4719190112, 4722238664, 4768579424, 4799782875, 4813637840, 4823747739, 4845714104, 4864759760, 4878780704, 4921491824, 4923510500, 4924118024, 4935148904, 4977874575, 5053883744.

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amicable numbers
友好的数字
https://www.numbersaplenty.com/set/amicable_number/

Two numbers (m,n) form an amicable pair if the sum of proper divisors of one number equals the other, i.e., if  σ(n)-n=m and σ(m)-m=n .
如果一个数n的真因数之和等于另一个数m，另一个数m的真因数之和等于第一个数n，即σ(n)-n=m 且 σ(m)-m=n，则这两个数形成友好对。

The first numbers which belong to an amicable pair
属于 友好对的第一个数字是
are 220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992 more terms

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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.

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