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pernicious n.  and  triangular n.

First numbers that belong to both sets:

3, 6, 10, 21, 28, 36, 55, 66, 91, 136, 171, 253, 276, 351, 406, 465, 496, 528, 595, 666, 820, 861, 1081, 1225, 1378, 1431, 1485, 1540, 1653, 1770, 1891, 2080, 2211, 2346, 2485, 2850, 3160, 3240, 3403, 3655, 3916, 4186, 4371, 4560, 4753, 4950, 5151, 5253, 5356, 5671, 6786, 7260, 7750, 8001, 8128, 8256, 8515, 8778, 9045, 9316, 9870, 10296, 10440, 10585, 11476, 12403, 12561, 12880, 13366, 13695, 13861, 14365, 16110, 16653, 16836, 17020, 17205, 17766, 18145, 18721, 19110, 21321, 21528, 21736, 22791, 23871, 24310, 24531, 24976, 25425, 25651, 25878, 26335, 26796, 27028, 27730, 29890, 30135, 32896, 33411, 33930, 34453, 34980, 35778, 38226, 38781, 41041, 41616, 43660, 46360, 48828, 49141, 49770, 51040, 51360, 53301, 53956, 54285, 56953, 60378, 61776, 62481, 62835, 63190, 64980, 65341, 67161, 67528, 68265, 68635, 70500, 71631, 72010, 72771, 73536, 74305, 75078, 77815, 80200, 81406, 82215, 85491, 86736, 87990, 88831, 92665, 95266, 96141, 97461, 97903, 98346, 99681, 101025, 102378, 104196, 109278, 111628, 112101, 114003, 114481, 114960, 117855, 118828, 119316, 119805, 120786, 122265, 124251, 124750, 126253, 128271, 131328, 132355, 133386, 134421, 135460, 137026, 139656, 141246, 142311, 143380, 143916, 144453, 144991, 148240, 148785, 151525, 152628, 154846, 161028, 161596, 162165, 162735, 163878, 164451, 165600, 166176, 167910, 168490, 171991, 173755, 174345, 176121, 177906, 184528, 186355, 187578, 188191, 189420, 190653, 191271, 193131, 193753, 195000, 196251, 198135, 200661, 203841, 205120, 210925, 217470, 218130, 218791, 219453, 220116, 220780, 221445, 228826, 232903, 234955, 237016, 237705, 238395, 243253, 243951, 251695, 252405, 253828, 255255, 261003, 262450, 263175, 264628, 267546, 268278, 271216, 271953, 273430, 274170, 274911, 278631, 279378, 281625, 282376, 296065, 297606, 303031, 303810, 306153, 306936, 315615, 319600, 322003, 324415, 325221, 326836, 328455, 329266, 331705, 333336, 334971, 339076, 340725, 341551, 344035, 344865, 345696, 346528, 348195, 350703.

Some larger examples :