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gapful n.  and  tetrahedral n.

First numbers that belong to both sets:

120, 165, 220, 286, 1140, 1330, 1540, 1771, 2300, 2600, 2925, 3276, 4960, 7140, 7770, 10660, 11480, 13244, 14190, 15180, 16215, 17296, 18424, 19600, 20825, 22100, 23426, 27720, 29260, 39711, 43680, 45760, 73150, 76076, 79079, 82160, 88560, 102340, 117480, 121485, 125580, 142880, 147440, 152096, 161700, 166650, 171700, 187460, 192920, 215820, 227920, 253460, 266916, 280840, 287980, 295240, 325500, 333375, 400995, 410040, 428536, 487344, 497640, 551300, 573800, 695520, 818805, 848046, 893200, 1021384, 1038220, 1055240, 1107414, 1125180, 1143135, 1161280, 1179616, 1235780, 1254890, 1313400, 1333300, 1353400, 1394204, 1414910, 1435820, 1456935, 1478256, 1521520, 1565620, 1656360, 1679580, 1750540, 1774630, 1798940, 1848224, 1873200, 1898400, 1923825, 2001460, 2054360, 2108184, 2162940, 2275280, 2303960, 2332880, 2450980, 2511496, 2573000, 2604125, 2635500, 2763520, 2796160, 2895620, 2963220, 3136805, 3244140, 3317040, 3391024, 3428425, 3619560, 3658620, 3898895, 3981264, 4022880, 4278680, 4682360, 4728720, 5616324, 5668650, 5721300, 5989445, 6608580, 7084700, 7145775, 7207200, 7519610, 8373840, 8718875, 9073260, 10116344, 10271580, 10349790, 10507399, 10586800, 10666600, 10746800, 10989810, 11071620, 11153835, 11402920, 11571020, 11740764, 11826255, 11912160, 11998480, 12085216, 12172369, 12259940, 12347930, 12436340, 12704100, 12794200, 13067054, 13158860, 13343760, 13530384, 13718740, 13813570, 14004539, 14100680, 14197260, 14294280, 14587990, 14686780, 14885696, 14985824, 15086400, 15187425, 15288900, 15699320, 15803060, 16117020, 16222590, 16328620, 16435111, 16542064, 16649480, 16757360, 17083794, 17193540, 17414440, 17861900, 17974950, 18316960, 18431920, 18547360, 18779684, 18896570, 19013940, 19131795, 19488280, 19728380, 20214480, 20337240, 20708500, 20958500, 21210504, 21337260, 21464520, 21720556, 21978620, 22238720, 22500864, 22765060, 23299640, 23434580, 23570040, 24117100, 24255175, 24672560, 24953460, 25094706, 25521640, 25665020, 26098380, 26389980, 26831440, 26979680, 27277796, 27578100, 27729075, 27880600, 28492220, 29112720, 29269240, 29426320, 30220155, 30380616, 31519775, 31684800, 31850400, 33196020, 33366840, 34930665, 35107380, 36724710, 37830065, 38016420, 38390964, 39721230, 39913740, 40495000, 40690000, 41873160, 43282239, 43486080, 43690560, 43895680, 45349524, 45559800, 46835120, 47049960, 49013160, 49456716, 50127055, 50577296, 51257700, 51485850, 54040336, 55709115, 56921900, 57166550, 57411900, 60665605, 61949040, 62207880, 62467440, 64569960, 66719136, 67263780.

Some larger examples :