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arithmetic n.  and  tetrahedral n.

First numbers that belong to both sets:

1, 20, 35, 56, 165, 220, 286, 455, 969, 1140, 1330, 1540, 1771, 2024, 3654, 4060, 4495, 4960, 5984, 6545, 7140, 7770, 9139, 10660, 11480, 12341, 13244, 14190, 15180, 16215, 18424, 20825, 22100, 24804, 26235, 27720, 29260, 30856, 32509, 34220, 35990, 37820, 39711, 43680, 45760, 47905, 50116, 52394, 54740, 57155, 59640, 62196, 73150, 76076, 79079, 82160, 85320, 88560, 91881, 95284, 98770, 102340, 105995, 109736, 113564, 117480, 121485, 125580, 129766, 134044, 138415, 142880, 147440, 156849, 166650, 171700, 176851, 182104, 187460, 192920, 198485, 204156, 209934, 215820, 221815, 234136, 240464, 246905, 253460, 260130, 266916, 273819, 280840, 287980, 302621, 310124, 317750, 325500, 333375, 341376, 366145, 374660, 383306, 392084, 400995, 419220, 428536, 437989, 447580, 457310, 467180, 477191, 497640, 508080, 518665, 562475, 573800, 585276, 596904, 608685, 620620, 632710, 657359, 669920, 695520, 708561, 721764, 735130, 748660, 762355, 776216, 790244, 804440, 818805, 833340, 848046, 862924, 877975, 893200, 908600, 924176, 939929, 955860, 971970, 988260, 1004731, 1021384, 1038220, 1055240, 1072445, 1089836, 1107414, 1125180, 1143135, 1179616, 1198144, 1216865, 1235780, 1274196, 1293699, 1313400, 1373701, 1394204, 1414910, 1435820, 1456935, 1499784, 1521520, 1543465, 1565620, 1587986, 1610564, 1633355, 1656360, 1703016, 1726669, 1750540, 1774630, 1798940, 1823471, 1848224, 1898400, 1923825, 1949476, 1975354, 2001460, 2027795, 2054360, 2081156, 2135445, 2162940, 2190670, 2218636, 2246839, 2275280, 2303960, 2450980, 2481115, 2511496, 2542124, 2573000, 2604125, 2635500, 2667126, 2699004, 2731135, 2763520, 2862209, 2895620, 2929290, 2963220, 2997411, 3031864, 3066580, 3101560, 3136805, 3172316, 3208094, 3244140, 3280455, 3353896, 3428425, 3466100, 3504050, 3542276, 3580779, 3619560, 3658620, 3697960, 3737581, 3777484, 3817670, 3858140, 3898895, 3939936, 4022880, 4064785, 4106980, 4192244, 4235315, 4322340, 4410549, 4455100, 4499950, 4590551, 4636304, 4728720, 4775385, 4822356, 4869634, 4917220, 4965115, 5013320, 5061836, 5159805, 5209260, 5259030, 5309116, 5359519, 5461280, 5564321, 5616324, 5668650, 5881204, 5935160, 5989445, 6044060, 6099006, 6154284, 6209895, 6322120, 6435689, 6492980, 6550610, 6608580, 6666891, 6725544, 6784540, 6843880, 6903565.

Some larger examples :