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amenable n.  and  tetrahedral n.

First numbers that belong to both sets:

1, 20, 56, 84, 120, 165, 220, 364, 560, 680, 816, 969, 1140, 1540, 2024, 2300, 2600, 2925, 3276, 4060, 4960, 5456, 5984, 6545, 7140, 8436, 9880, 10660, 11480, 12341, 13244, 15180, 17296, 18424, 19600, 20825, 22100, 24804, 27720, 29260, 30856, 32509, 34220, 37820, 41664, 43680, 45760, 47905, 50116, 54740, 59640, 62196, 64824, 67525, 70300, 76076, 82160, 85320, 88560, 91881, 95284, 102340, 109736, 113564, 117480, 121485, 125580, 134044, 142880, 147440, 152096, 156849, 161700, 171700, 182104, 187460, 192920, 198485, 204156, 215820, 227920, 234136, 240464, 246905, 253460, 266916, 280840, 287980, 295240, 302621, 310124, 325500, 341376, 349504, 357760, 366145, 374660, 392084, 410040, 419220, 428536, 437989, 447580, 467180, 487344, 497640, 508080, 518665, 529396, 551300, 573800, 585276, 596904, 608685, 620620, 644956, 669920, 682640, 695520, 708561, 721764, 748660, 776216, 790244, 804440, 818805, 833340, 862924, 893200, 908600, 924176, 939929, 955860, 988260, 1021384, 1038220, 1055240, 1072445, 1089836, 1125180, 1161280, 1179616, 1198144, 1216865, 1235780, 1274196, 1313400, 1333300, 1353400, 1373701, 1394204, 1435820, 1478256, 1499784, 1521520, 1543465, 1565620, 1610564, 1656360, 1679580, 1703016, 1726669, 1750540, 1798940, 1848224, 1873200, 1898400, 1923825, 1949476, 2001460, 2054360, 2081156, 2108184, 2135445, 2162940, 2218636, 2275280, 2303960, 2332880, 2362041, 2391444, 2450980, 2511496, 2542124, 2573000, 2604125, 2635500, 2699004, 2763520, 2796160, 2829056, 2862209, 2895620, 2963220, 3031864, 3066580, 3101560, 3136805, 3172316, 3244140, 3317040, 3353896, 3391024, 3428425, 3466100, 3542276, 3619560, 3658620, 3697960, 3737581, 3777484, 3858140, 3939936, 3981264, 4022880, 4064785, 4106980, 4192244, 4278680, 4322340, 4366296, 4410549, 4455100, 4545100, 4636304, 4682360, 4728720, 4775385, 4822356, 4917220, 5013320, 5061836, 5110664, 5159805, 5209260, 5309116, 5410240, 5461280, 5512640, 5564321, 5616324, 5721300, 5827576, 5881204, 5935160, 5989445, 6044060, 6154284, 6265840, 6322120, 6378736, 6435689, 6492980, 6608580, 6725544, 6784540, 6843880, 6903565, 6963596, 7084700, 7207200, 7268976, 7331104, 7393585, 7456420, 7583156, 7711320, 7775940, 7840920, 7906261, 7971964, 8104460, 8238416, 8305944, 8373840, 8442105, 8510740, 8649124, 8789000, 8859500.

Some larger examples :