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interprime n.  and  triangular n.

First numbers that belong to both sets:

6, 15, 21, 45, 105, 120, 231, 300, 351, 465, 741, 780, 861, 1176, 1431, 1485, 3081, 3240, 3321, 3828, 4005, 4278, 5460, 6786, 6903, 7140, 7381, 7503, 7875, 8001, 10731, 11175, 11325, 11781, 12246, 12561, 13530, 13695, 14535, 14706, 17205, 17391, 18915, 21321, 22155, 23871, 30135, 30876, 31878, 32640, 33411, 36585, 39621, 40755, 42195, 43956, 44253, 45150, 46056, 47586, 49455, 49770, 51681, 58311, 60378, 67896, 69006, 71253, 80601, 84255, 84666, 86736, 87571, 88831, 89676, 90525, 92235, 94830, 97461, 98790, 106953, 108345, 109746, 112575, 119316, 122265, 130305, 139128, 146070, 147696, 158766, 162735, 166176, 169653, 170820, 172578, 177310, 190653, 198765, 201930, 205120, 205761, 206403, 208335, 214840, 216153, 222111, 229503, 231540, 235641, 250986, 252405, 267546, 269011, 269745, 271953, 280875, 281625, 286146, 288420, 303810, 306153, 309291, 315615, 318801, 321201, 353220, 360825, 378015, 391170, 407253, 432915, 440391, 457446, 468996, 474825, 475800, 477753, 483636, 489555, 499500, 511566, 520710, 522753, 545490, 546535, 564453, 570846, 574056, 577275, 598965, 606651, 612171, 615495, 618828, 623286, 630003, 635628, 659526, 664128, 666435, 671061, 678030, 679195, 685035, 714610, 715806, 726615, 735078, 748476, 753378, 757065, 763230, 766941, 768180, 781875, 783126, 793170, 795691, 808356, 836571, 846951, 862641, 870540, 882456, 906531, 920046, 922761, 936396, 955653, 959805, 962578, 980700, 982101, 986310, 989121, 997578, 1007490, 1016025, 1023165, 1037520, 1044735, 1046181, 1054878, 1063611, 1097421, 1115271, 1121253, 1142316, 1154440, 1166628, 1169685, 1180416, 1188111, 1197378, 1202025, 1203576, 1206681, 1228528, 1234806, 1268028, 1269621, 1274406, 1342341, 1350546, 1365378, 1385280, 1396956, 1400301, 1405326, 1425516, 1433971, 1497315, 1519896, 1540890, 1610115, 1619100, 1626306, 1653471, 1657110, 1662576, 1666225, 1673535, 1675365, 1693720, 1701090, 1712175, 1714026, 1758750, 1773786, 1804050, 1819278, 1821186, 1832655, 1853775, 1906128, 1910035, 1979055, 1983036, 2007006, 2013021, 2025078, 2051325, 2057406, 2122830, 2141415, 2143485, 2147628, 2153850, 2160081, 2168403, 2174655, 2180916, 2212356, 2235555, 2248260, 2263128, 2280180, 2299440, 2301585.

Some larger examples :