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heptagonal n.  and  interprime n.

First numbers that belong to both sets:

18, 34, 81, 342, 1404, 2205, 2512, 7209, 8323, 17514, 20115, 23863, 35224, 35820, 37638, 39501, 42706, 53802, 56776, 89019, 100701, 106812, 125104, 126225, 129618, 136539, 137710, 138886, 143640, 147258, 155875, 158382, 167314, 169911, 206928, 214183, 233631, 255520, 258727, 270109, 307476, 309232, 334341, 336172, 338008, 351000, 354757, 360430, 379665, 389470, 391446, 415548, 429940, 434097, 448804, 478953, 481144, 512343, 516880, 519156, 523723, 580087, 584914, 589761, 649485, 652036, 704106, 739024, 755425, 794394, 800041, 817102, 896104, 1019844, 1039095, 1048788, 1068309, 1071580, 1081423, 1097928, 1114558, 1127952, 1178892, 1259185, 1262736, 1269853, 1273419, 1291324, 1367890, 1371591, 1393902, 1408876, 1626912, 1800729, 1852011, 1952314, 2001220, 2010177, 2023650, 2110024, 2119221, 2133054, 2259576, 2273859, 2283406, 2336272, 2429011, 2433942, 2488513, 2574040, 2599470, 2604571, 2609677, 2887450, 2946861, 3061962, 3095253, 3196206, 3316032, 3420495, 3455676, 3467443, 3526578, 3538465, 3652389, 3676603, 3713074, 3817386, 3891888, 3992344, 4011322, 4023999, 4081293, 4094080, 4262131, 4314519, 4340833, 4466917, 4745143, 4800411, 4904901, 5348728, 5400045, 5422113, 5781321, 5834668, 5895936, 6011676, 6333772, 6453712, 6656112, 6688786, 6705153, 6886510, 6969745, 7011550, 7180020, 7583797, 7767778, 7873900, 7945048, 8151381, 8214703, 8278270, 8351218, 8378656, 8636914, 8786250, 8927415, 9098298, 9290068, 9454645, 9561906, 9738729, 9917172, 10218177, 10278918, 10575037, 10927566, 10948483, 11021850, 11063884, 11127085, 11179890, 11563776, 11606830, 11628387, 11790702, 11845057, 11954142, 11965078, 12008872, 12041770, 12096700, 12251169, 12306574, 12317670, 12440056, 12822165, 12856158, 12878845, 12981184, 13244557, 13348336, 13627060, 14181237, 14396400, 14432418, 15372280, 15571296, 15784153, 15796719, 16137891, 16163308, 16367364, 16637130, 16675848, 16688764, 17446447, 17525788, 17605309, 17685010, 17724928, 17898426, 17938584, 17978787, 18059328, 18193963, 18369736, 18751194, 18874638, 18970930, 18984706, 19081278, 19122741, 19330731, 19919088, 20003859, 20117167, 20444710, 20904822, 21006154, 21487162, 21604590, 21633997, 21869973, 22122100, 22181634, 22330819, 22570555, 22615648, 22690903, 22721040, 23099440, 23343256, 23496291, 23742187, 23865615, 24425001, 24659991, 25196800, 25467372, 25579204, 26336421, 26401375, 26596717, 26727345, 27022428, 27137620, 27269568, 27385285, 27468090, 27950824, 28084732, 28101493, 28252567, 28471500, 28539034, 28572831, 28725165.

Some larger examples :