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Friedman n.  and  Ulam n.

First numbers that belong to both sets:

126, 688, 1296, 1792, 2916, 4167, 4536, 4624, 7928, 8192, 10525, 12060, 12595, 12600, 12768, 13689, 14129, 14168, 15617, 15620, 15622, 15642, 15661, 15688, 16245, 16372, 16783, 17328, 17689, 17892, 18432, 19629, 19642, 19683, 20736, 21753, 21870, 23392, 24367, 25105, 25921, 27634, 32685, 32751, 32875, 33696, 36457, 39294, 45361, 45364, 45366, 45684, 46556, 46593, 46615, 48750, 54436, 57288, 59057, 59059, 59147, 59313, 59318, 63985, 65344, 65542, 73984, 74358, 78133, 78135, 81920, 86142, 87381, 91853, 97336, 97343, 98325, 102391, 102912, 103689, 104879, 104925, 104984, 104986, 106929, 107835, 108612, 112590, 114772, 114921, 116478, 116827, 117597, 117641, 117643, 117660, 117726, 120060, 124468, 124751, 125008, 125010, 125030, 125032, 125049, 125052, 125054, 125071, 125074, 125076, 125096, 125098, 126027, 127253, 127449, 127583, 127620, 128485, 129609, 132250, 132565, 132675, 132678, 134799, 135837, 136590, 137281, 137772, 137802, 137816, 139676, 141376, 141750, 143739, 145117, 146329, 146378, 146952, 147456, 149283, 149396, 151272, 154275, 154950, 155277, 155468, 156245, 156247, 156550, 157950, 159358, 159375, 162036, 162072, 164775, 165874, 165879, 166248, 166439, 167042, 167384, 167932, 167961, 167968, 168259, 169398, 172386, 172872, 174280, 174820, 175560, 175616, 176699, 179250, 179335, 179428, 185344, 186573, 186617, 186619, 186636, 186639, 186641, 187440, 187653, 193742, 194245, 194392, 194485, 194487, 194724, 194976, 195286, 195298, 195736, 196249, 196425, 196488, 196530, 196554, 196581, 196615, 196618, 196662, 196830, 196833, 196835, 197370, 197505, 197725, 198450, 198472, 201756, 204911, 205387, 209944, 210125, 210147, 210743, 214355, 215044, 215046, 215694, 215784, 216016, 216036, 216038, 216058, 216060, 216099, 221849, 224532, 224673, 224676, 226579, 228478, 228546, 229367, 229736, 229888, 230144, 233255, 234327, 234357, 234374, 234379, 235246, 235378, 236219, 236754, 236756, 237699, 238462, 238464, 240099, 240991, 245157, 245460, 245763, 245765, 245963, 246518, 247099, 248568, 248656, 248758, 248783, 248785, 250022, 250024, 250036, 250053, 250056, 250061, 250063, 250080, 251050, 252003, 252648, 253125.

Some larger examples :