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interprime n.  and  octagonal n.

First numbers that belong to both sets:

21, 176, 225, 560, 645, 736, 1281, 1976, 2640, 4256, 7701, 11781, 15841, 25761, 49665, 64533, 65416, 67200, 93633, 101200, 106785, 117216, 124440, 128133, 144760, 150080, 163800, 166616, 168033, 185505, 205408, 213333, 218160, 224680, 226325, 231296, 243105, 246533, 265816, 285825, 318176, 326040, 330008, 354320, 375240, 455520, 464920, 513360, 535941, 585208, 628376, 633880, 647745, 664581, 678776, 698901, 737056, 797736, 857605, 860816, 864033, 870485, 883461, 932976, 953160, 956545, 1018501, 1093240, 1111425, 1115080, 1122408, 1129760, 1193221, 1223685, 1262305, 1281840, 1293633, 1305480, 1321360, 1357441, 1365525, 1373633, 1377696, 1385840, 1426920, 1443520, 1527960, 1536536, 1566741, 1579776, 1592865, 1659120, 1690501, 1754145, 1781781, 1823640, 1847105, 1870720, 1894485, 2085000, 2145456, 2206776, 2222241, 2248136, 2347905, 2374520, 2390561, 2412033, 2509845, 2598421, 2626416, 2677185, 2682856, 2797536, 2855776, 2938320, 2950208, 3137541, 3267720, 3400545, 3497040, 3555585, 3808133, 3882856, 3951416, 3992840, 4076336, 4167765, 4281685, 4296033, 4404408, 4551008, 4617761, 4715040, 4866680, 5153541, 5320008, 5384120, 5464800, 5546080, 5562408, 5578760, 5611536, 5944576, 6097576, 6200656, 6243861, 6252520, 6295905, 6348165, 6532776, 6693120, 6882645, 6973825, 7047201, 7495521, 7552533, 7581120, 7600208, 7724865, 8065520, 8605520, 8656405, 8933776, 8964865, 8975240, 9184000, 9331560, 9416408, 9427041, 9555105, 9662485, 9868160, 9977280, 10131056, 10308240, 10330496, 10531880, 10678533, 10689856, 11009336, 11020833, 11170840, 11205601, 11228805, 11310208, 11828616, 12152481, 12188736, 12212936, 12285680, 12407400, 12689633, 12714325, 12813333, 12962565, 13301496, 13339425, 13466245, 13708856, 14031381, 14357656, 14410208, 14462856, 14581665, 14647880, 14700960, 14714245, 15102120, 15372560, 15386145, 15535976, 15590640, 16142560, 16198280, 16268065, 16803333, 16845960, 17332840, 17448408, 17929185, 18061440, 18120376, 18431365, 18446240, 18505800, 18520705, 18700033, 18730005, 19152133, 19380208, 19441256, 19578965, 19655680, 19717160, 19763333, 19809560, 19824981, 20274800, 20792801, 20935208, 20982785, 21046305, 21141765, 21157696, 21413408, 21638416, 21670656, 21864600, 21929440, 22010625, 22157136, 22206081, 22435205, 22484456, 22930145, 23096325, 23329985, 24004065, 24021040, 24106005, 24773880, 24946600, 25172033, 25293840, 25398480, 25661025, 25819200, 25854416, 25977861, 26314408, 26349960, 26492408, 26528080, 26724705, 26814320, 26832261, 27174280, 27355160, 27427680.

Some larger examples :