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amicable n.  and  gapful n.

First numbers that belong to both sets:

220, 1210, 2620, 12285, 14595, 17296, 18416, 69615, 100485, 122265, 124155, 139815, 142310, 168730, 171856, 176336, 280540, 980984, 1077890, 1099390, 1125765, 1154450, 1156870, 1175265, 1185376, 1189150, 1280565, 1292570, 1328470, 1340235, 1358595, 1438983, 1466150, 1483850, 1486845, 1511930, 1598470, 1669910, 1747930, 1798875, 1870245, 2728726, 2803580, 4314616, 4482765, 5730615, 8619765, 9206925, 9773505, 10025290, 10043690, 10254970, 10273670, 10533296, 10572550, 10634085, 10791795, 10854650, 10893230, 10950615, 10992735, 11049730, 11173460, 11498355, 11545616, 11693290, 11791935, 12024045, 12070305, 13671735, 13813150, 14310050, 14426230, 14443730, 14654150, 15877065, 15882670, 15938055, 16817050, 17041010, 17257695, 17308665, 17578785, 17754165, 17844255, 18017056, 18194715, 19154336, 19895265, 19985355, 22227075, 23628940, 24472180, 24644925, 26090325, 26138475, 31536855, 32148585, 33501825, 35390008, 36939357, 37363095, 38400512, 40105845, 43266285, 46271745, 46521405, 49125375, 56924192, 63717615, 66011985, 67738268, 72958556, 79324875, 82633005, 82824255, 84591405, 102023145, 102358010, 102719740, 102814490, 107908335, 108734050, 109410345, 110132055, 110960710, 115259625, 116251550, 116654896, 118458830, 118458976, 120812175, 121293315, 123757335, 125222330, 126671985, 127924335, 131118975, 131483835, 132692805, 132926625, 133089500, 133178325, 133471275, 133768816, 134886465, 136549413, 136770075, 138605350, 138690045, 139009990, 140744835, 144788020, 147313850, 147366765, 147382335, 148532625, 149364256, 153015550, 154190750, 155578180, 155711205, 155797390, 156322490, 157151410, 163634510, 165195890, 165323696, 165742395, 166562685, 166706530, 166737550, 168392450, 169335790, 170566690, 172271385, 173843216, 176632390, 179029010, 181088985, 182028483, 182618810, 182622405, 183408615, 184694055, 186878110, 188953970, 190055385, 190888155, 194594085, 195857415, 196214265, 196323170, 196421715, 197261415, 197704670, 203055622, 207429525, 213484172, 227443340, 258904646, 271048340, 274638460, 301685895, 311414355, 312090808, 319904235, 327818272, 360027675, 362700728, 370393569, 385465395, 388904355, 391548675, 393463072, 395378272, 395939775, 397287345, 399052815, 400250565, 405370035, 419640364, 426191535, 426386025, 426684375, 433850085, 436386015, 442792251, 458447924, 465418845, 467406225, 473836365, 475838415, 482909985, 506468950, 512412550, 522145832, 528145850, 537882550, 551388915, 557346712, 570975050, 579980048, 613290028, 637756665, 640866135, 646745463, 651016665, 663576615, 664747083, 673747893, 700743825, 705280310, 724885425, 728921270, 750610875, 750893325, 752458216, 786508275, 925581105, 934224585, 965615992, 966751929, 972264184, 990788572, 1002372250, 1002455350, 1005541130, 1008990045, 1015866225, 1018330430, 1020658815, 1025532496, 1031796176, 1038911296, 1040792450, 1044659750, 1045525275, 1047381370, 1048124570.

Some larger examples :