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odious n.  and  tetrahedral n.

First numbers that belong to both sets:

1, 4, 35, 56, 84, 220, 286, 364, 560, 1140, 1330, 1540, 2024, 2300, 4060, 4495, 4960, 5456, 11480, 13244, 16215, 17296, 18424, 19600, 20825, 22100, 23426, 29260, 32509, 34220, 35990, 37820, 41664, 50116, 54740, 59640, 70300, 73150, 76076, 85320, 88560, 98770, 102340, 105995, 113564, 117480, 125580, 147440, 152096, 182104, 192920, 198485, 204156, 221815, 227920, 240464, 260130, 280840, 287980, 295240, 310124, 325500, 333375, 341376, 349504, 419220, 457310, 467180, 529396, 551300, 562475, 573800, 585276, 596904, 620620, 657359, 695520, 748660, 776216, 790244, 818805, 848046, 893200, 924176, 955860, 988260, 1004731, 1021384, 1038220, 1055240, 1072445, 1089836, 1107414, 1161280, 1179616, 1198144, 1254890, 1394204, 1435820, 1499784, 1543465, 1565620, 1587986, 1633355, 1726669, 1774630, 1823471, 1848224, 1873200, 1923825, 1949476, 2108184, 2135445, 2190670, 2275280, 2303960, 2332880, 2362041, 2391444, 2450980, 2481115, 2573000, 2635500, 2667126, 2699004, 2763520, 2895620, 2963220, 2997411, 3101560, 3208094, 3580779, 3619560, 3658620, 3737581, 3817670, 3858140, 3898895, 4064785, 4106980, 4149466, 4235315, 4322340, 4410549, 4636304, 4775385, 4917220, 5110664, 5259030, 5309116, 5410240, 5461280, 5512640, 5616324, 5774275, 5935160, 5989445, 6099006, 6209895, 6265840, 6322120, 6435689, 6608580, 6666891, 6725544, 6784540, 6963596, 7023974, 7084700, 7268976, 7331104, 7456420, 7519610, 7906261, 7971964, 8038030, 8171255, 8238416, 8373840, 8718875, 8789000, 8859500, 9073260, 9145270, 9437120, 9511040, 9735114, 9810580, 10116344, 10193765, 10507399, 10586800, 10666600, 10827401, 10908404, 10989810, 11071620, 11319484, 11402920, 11486765, 11571020, 11655686, 11826255, 12172369, 12259940, 12704100, 12794200, 12884725, 12975676, 13067054, 13158860, 13251095, 13530384, 13624345, 13718740, 13813570, 14100680, 14197260, 14489644, 14587990, 14885696, 15390826, 15493204, 15699320, 15803060, 16011909, 16117020, 16542064, 16649480, 16757360, 17193540, 17525596, 17749325, 18088476, 18202479, 18316960, 18431920, 18663281, 18779684, 18896570, 19368964, 19488280, 19608085, 19849166, 19970444, 20092215, 20214480, 20337240, 20460496, 20584249, 20708500, 20833250, 21337260, 21464520, 21720556, 21978620, 22108415, 22238720, 22369536, 23299640, 23979550, 24117100, 24255175, 24953460, 25094706, 25521640, 25808936, 26098380, 26243910, 26683744, 26831440, 26979680, 27277796, 27427674, 28032676, 28492220, 28801356, 28956759, 29426320, 29583961.

Some larger examples :