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hexagonal n.  and  unprimeable n.

First numbers that belong to both sets:

325, 3486, 4186, 5995, 7140, 10296, 10878, 14706, 18336, 19110, 19900, 21115, 26796, 30628, 34716, 35245, 39060, 41328, 47895, 48516, 49770, 56280, 59685, 61075, 61776, 73536, 74305, 78210, 84666, 103740, 105570, 107416, 110215, 111156, 118828, 120786, 128778, 132870, 140185, 147696, 161028, 162165, 173755, 179700, 186966, 195625, 217470, 220116, 228150, 233586, 244650, 251695, 253116, 264628, 270480, 276396, 279378, 285390, 291466, 296065, 300700, 306936, 310078, 313236, 316410, 332520, 335790, 345696, 355746, 369370, 374545, 376278, 383250, 386760, 393828, 395605, 397386, 408156, 415416, 419070, 441330, 450775, 460320, 464166, 479710, 483636, 487578, 511566, 525825, 527878, 536130, 544446, 546535, 571915, 582660, 591328, 600060, 604450, 626640, 635628, 640146, 649230, 656085, 660675, 662976, 667590, 679195, 690900, 695610, 719400, 724206, 755835, 768180, 780625, 788140, 793170, 798216, 813450, 823686, 826255, 833986, 849556, 857395, 865270, 878475, 881128, 886446, 891780, 902496, 918690, 924120, 932295, 937765, 951510, 962578, 973710, 979300, 984906, 1013176, 1021735, 1030330, 1036080, 1047628, 1059240, 1070916, 1073845, 1088550, 1106328, 1112286, 1136278, 1160526, 1163575, 1166628, 1185030, 1194285, 1197378, 1200475, 1209790, 1228528, 1234806, 1241100, 1260078, 1279200, 1311390, 1317876, 1321125, 1324378, 1330896, 1370340, 1383616, 1390278, 1396956, 1417086, 1420455, 1423828, 1427205, 1437360, 1444150, 1450956, 1454365, 1457778, 1471470, 1478340, 1492128, 1495585, 1512930, 1530375, 1540890, 1554966, 1558495, 1562028, 1576200, 1594005, 1597578, 1601155, 1619100, 1633528, 1655290, 1666225, 1673535, 1691880, 1710325, 1714026, 1736316, 1743778, 1751256, 1758750, 1766260, 1796460, 1804050, 1834570, 1842240, 1857628, 1861485, 1873080, 1896378, 1919820, 1935528, 1939465, 1943406, 1959210, 1983036, 1991010, 2047276, 2055378, 2059435, 2104326, 2133145, 2153850, 2162160, 2174655, 2183005, 2187186, 2229216, 2263128, 2271646, 2280180, 2305878, 2310175, 2314476, 2331720, 2383836, 2388205, 2445366, 2463090, 2471976, 2516646, 2521135, 2530125, 2561716, 2579856, 2588950, 2598060, 2616328, 2634660, 2657665, 2671516, 2717946, 2727280, 2745996, 2750685, 2755378, 2764776, 2774190, 2783620, 2802528, 2807265, 2840536, 2854855, 2878800, 2888406, 2902845, 2907666, 2917320, 2926990, 2936676, 2941525, 2965830, 2975580, 2985346.

Some larger examples :