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amenable n.  and  triangular n.

First numbers that belong to both sets:

1, 21, 28, 36, 45, 105, 120, 136, 153, 253, 276, 300, 325, 465, 496, 528, 561, 741, 780, 820, 861, 1081, 1128, 1176, 1225, 1485, 1540, 1596, 1653, 1953, 2016, 2080, 2145, 2485, 2556, 2628, 2701, 3081, 3160, 3240, 3321, 3741, 3828, 3916, 4005, 4465, 4560, 4656, 4753, 5253, 5356, 5460, 5565, 6105, 6216, 6328, 6441, 7021, 7140, 7260, 7381, 8001, 8128, 8256, 8385, 9045, 9180, 9316, 9453, 10153, 10296, 10440, 10585, 11325, 11476, 11628, 11781, 12561, 12720, 12880, 13041, 13861, 14028, 14196, 14365, 15225, 15400, 15576, 15753, 16653, 16836, 17020, 17205, 18145, 18336, 18528, 18721, 19701, 19900, 20100, 20301, 21321, 21528, 21736, 21945, 23005, 23220, 23436, 23653, 24753, 24976, 25200, 25425, 26565, 26796, 27028, 27261, 28441, 28680, 28920, 29161, 30381, 30628, 30876, 31125, 32385, 32640, 32896, 33153, 34453, 34716, 34980, 35245, 36585, 36856, 37128, 37401, 38781, 39060, 39340, 39621, 41041, 41328, 41616, 41905, 43365, 43660, 43956, 44253, 45753, 46056, 46360, 46665, 48205, 48516, 48828, 49141, 50721, 51040, 51360, 51681, 53301, 53628, 53956, 54285, 55945, 56280, 56616, 56953, 58653, 58996, 59340, 59685, 61425, 61776, 62128, 62481, 64261, 64620, 64980, 65341, 67161, 67528, 67896, 68265, 70125, 70500, 70876, 71253, 73153, 73536, 73920, 74305, 76245, 76636, 77028, 77421, 79401, 79800, 80200, 80601, 82621, 83028, 83436, 83845, 85905, 86320, 86736, 87153, 89253, 89676, 90100, 90525, 92665, 93096, 93528, 93961, 96141, 96580, 97020, 97461, 99681, 100128, 100576, 101025, 103285, 103740, 104196, 104653, 106953, 107416, 107880, 108345, 110685, 111156, 111628, 112101, 114481, 114960, 115440, 115921, 118341, 118828, 119316, 119805, 122265, 122760, 123256, 123753, 126253, 126756, 127260, 127765, 130305, 130816, 131328, 131841, 134421, 134940, 135460, 135981, 138601, 139128, 139656, 140185, 142845, 143380, 143916, 144453, 147153, 147696, 148240, 148785, 151525, 152076, 152628, 153181, 155961, 156520, 157080.

Some larger examples :