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triangular n.  and  unprimeable n.

First numbers that belong to both sets:

325, 2485, 3240, 3486, 4186, 5460, 5995, 7140, 7260, 8256, 10296, 10440, 10878, 14706, 15576, 16290, 18336, 19110, 19900, 20910, 21115, 25200, 26796, 27028, 27495, 29890, 30628, 32896, 34716, 35245, 36046, 37675, 38226, 39060, 41328, 43365, 45150, 46360, 47895, 48205, 48516, 49770, 52650, 55278, 56280, 59685, 61075, 61425, 61776, 62835, 64980, 72390, 73536, 73920, 74305, 75466, 78210, 84255, 84666, 85078, 86736, 98790, 100576, 102378, 103740, 104196, 105570, 107416, 110215, 111156, 113526, 115440, 118828, 120786, 125250, 128778, 132355, 132870, 137550, 139656, 140185, 143916, 147696, 161028, 162165, 165025, 166176, 173166, 173755, 179700, 186355, 186966, 192510, 195000, 195625, 201295, 207690, 217470, 220116, 224785, 228150, 233586, 244650, 245350, 250986, 251695, 253116, 259560, 264628, 265356, 266815, 270480, 276396, 277140, 279378, 285390, 286146, 291466, 296065, 299925, 300700, 306936, 307720, 310078, 312445, 313236, 316410, 323610, 328455, 330078, 331705, 332520, 335790, 343206, 345696, 349866, 353220, 355746, 359976, 369370, 370230, 373680, 374545, 376278, 383250, 384126, 386760, 393828, 395605, 396495, 397386, 401856, 405450, 408156, 412686, 415416, 416328, 419070, 419986, 432915, 434778, 441330, 450775, 453628, 457446, 460320, 461280, 464166, 468996, 472878, 474825, 476776, 479710, 480690, 483636, 487578, 496506, 504510, 511566, 514605, 516636, 525825, 527878, 528906, 533028, 536130, 541320, 544446, 546535, 549676, 555985, 566580, 571915, 572985, 582660, 583740, 591328, 592416, 594595, 600060, 601156, 604450, 609960, 616605, 626640, 627760, 635628, 636756, 640146, 645816, 649230, 650370, 656085, 660675, 662976, 667590, 679195, 687378, 690900, 695610, 719400, 724206, 725410, 754606, 755835, 764466, 768180, 774390, 780625, 781875, 788140, 793170, 794430, 798216, 813450, 814726, 819840, 823686, 826255, 833986, 837865, 849556, 850860, 857395, 861328, 865270, 877150, 878475, 881128, 885115, 886446, 887778, 891780, 902496, 909226, 911925, 918690, 920046, 924120, 932295, 937765, 939135, 951510, 952890, 962578, 963966, 966745, 969528, 973710, 975106, 979300, 980700, 984906, 986310, 1003236, 1013176, 1014600, 1021735, 1030330, 1036080.

Some larger examples :