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deficient n.  and  pentagonal n.

First numbers that belong to both sets:

1, 5, 22, 35, 51, 92, 117, 145, 247, 287, 376, 425, 477, 590, 651, 715, 782, 925, 1001, 1162, 1247, 1335, 1426, 1617, 1717, 2035, 2147, 2501, 2625, 2882, 3015, 3151, 3577, 3725, 4187, 4347, 4845, 5017, 5551, 5735, 6112, 6305, 6501, 6902, 7107, 7315, 7526, 7957, 8177, 8626, 8855, 9087, 9322, 9801, 10045, 10292, 10795, 11051, 11572, 11837, 12105, 12927, 13207, 13490, 14065, 14357, 15251, 15555, 15862, 16172, 16485, 16801, 17767, 18095, 19097, 19437, 20126, 20827, 21182, 21901, 22265, 23002, 23375, 23751, 24130, 24512, 24897, 25285, 26467, 26867, 28085, 28497, 29751, 30175, 30602, 31465, 31901, 32782, 33227, 33675, 34126, 35037, 35497, 36895, 37367, 38801, 39285, 39772, 40262, 40755, 41251, 41750, 42757, 43265, 44290, 44807, 45327, 46905, 47437, 47972, 49051, 49595, 50692, 51245, 51801, 52922, 53487, 54055, 54626, 55777, 56357, 57526, 58115, 58707, 59302, 60501, 61105, 62935, 63551, 65417, 66045, 66676, 67310, 67947, 68587, 70525, 71177, 72490, 73151, 73815, 74482, 75825, 76501, 78547, 79235, 81317, 82017, 83426, 84135, 84847, 85562, 87001, 87725, 89182, 89915, 90651, 92132, 92877, 93625, 94376, 95887, 96647, 98945, 99717, 102051, 102835, 103622, 105205, 106001, 107602, 108407, 109215, 110026, 111657, 112477, 114955, 115787, 118301, 119145, 119992, 120842, 121695, 122551, 125137, 126005, 128627, 129507, 131276, 132165, 133057, 135751, 136655, 138472, 139385, 140301, 143067, 143995, 144926, 146797, 147737, 149626, 150575, 151527, 152482, 154401, 155365, 158275, 159251, 161212, 162197, 163185, 165170, 166167, 167167, 168170, 170185, 171197, 173230, 174251, 175275, 176302, 177332, 178365, 179401, 182527, 183575, 186737, 187797, 189926, 190995, 192067, 193142, 195301, 196385, 198562, 199655, 200751, 202952, 204057, 205165, 208507, 209627, 213005, 214137, 215272, 217551, 218695, 219842, 222145, 223301, 225622, 226787, 227955, 229126, 231477, 232657, 236215, 237407, 241001, 242205, 243412, 244622, 245835, 247051, 250717, 251945, 255647, 256887, 258130, 260625.

Some larger examples :