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pseudoperfect n.  and  triangular n.

First numbers that belong to both sets:

6, 28, 36, 66, 78, 120, 210, 276, 300, 378, 496, 528, 630, 666, 780, 820, 990, 1128, 1176, 1326, 1540, 1596, 1770, 1830, 2016, 2080, 2346, 2556, 2628, 2850, 3160, 3240, 3486, 3570, 3828, 4095, 4278, 4560, 4656, 4950, 5460, 5778, 5886, 6216, 6328, 6786, 7140, 7260, 7626, 7875, 8128, 8256, 8646, 8778, 9180, 9730, 9870, 10296, 10440, 10878, 11628, 12090, 12246, 12720, 12880, 13530, 14028, 14196, 14706, 15400, 15576, 16110, 16290, 16836, 17020, 17766, 17955, 18336, 18528, 19110, 19900, 20100, 20706, 20910, 21528, 21736, 21945, 22578, 23220, 23436, 24090, 24310, 24976, 25200, 25878, 26106, 26565, 26796, 27966, 28680, 28920, 29646, 29890, 30628, 30876, 31626, 31878, 32640, 33670, 33930, 34716, 34980, 35778, 37128, 37950, 38226, 39060, 39340, 40470, 41328, 41616, 42486, 43660, 43956, 44850, 45150, 46056, 46360, 47586, 48516, 48828, 49770, 51040, 51360, 52326, 52650, 53628, 53956, 54285, 55278, 56280, 56616, 57630, 57970, 58996, 59340, 60378, 60726, 61425, 61776, 62128, 63546, 64620, 64980, 66066, 66430, 67896, 69006, 69378, 70500, 72390, 73536, 73920, 75078, 76636, 77028, 78210, 78606, 79800, 80200, 81810, 82215, 83028, 83436, 84666, 86320, 86736, 87990, 88410, 89676, 90100, 91806, 93096, 93528, 94830, 96580, 97020, 98346, 98790, 100128, 100576, 101475, 102378, 103740, 104196, 105570, 107880, 109278, 109746, 111156, 113050, 113526, 114960, 115440, 116886, 119316, 120786, 121278, 122265, 122760, 123256, 125250, 126756, 127260, 128778, 130816, 131328, 132870, 133386, 134940, 135460, 137550, 139128, 139656, 141246, 143380, 143916, 145530, 146070, 147696, 148240, 150426, 152076, 152628, 154290, 156520, 157080, 158766, 159330, 161028, 163878, 165600, 166176, 167910, 168490, 170820, 172578, 173166, 174936, 176715, 177310, 177906, 179700, 180300, 182106, 184528, 185136, 186966, 187578, 189420, 190036, 192510, 194376, 195000, 196878, 198135, 200028, 201930, 202566, 204480, 205120, 207690, 209628, 210276, 211575, 212226, 214840, 215496, 217470, 218130.

Some larger examples :