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nude n.  and  Ulam n.

First numbers that belong to both sets:

1, 2, 3, 4, 6, 8, 11, 36, 48, 77, 99, 126, 155, 175, 324, 412, 612, 624, 864, 1155, 1164, 1296, 1311, 1335, 1944, 2112, 2288, 2616, 2916, 3288, 3393, 4368, 4392, 4644, 6366, 7476, 8128, 8424, 9135, 9162, 11226, 11622, 11688, 12162, 12248, 12336, 12624, 12768, 13164, 13848, 14212, 14364, 14488, 14664, 17115, 18432, 18488, 21132, 22122, 22124, 22344, 22488, 23136, 23226, 24824, 24888, 26376, 27412, 28296, 29232, 29916, 31128, 31326, 31368, 31644, 31773, 32316, 32448, 32922, 33117, 33696, 33726, 36396, 36636, 37464, 39492, 39915, 41124, 41212, 42192, 42212, 42324, 43116, 43248, 44848, 46488, 48384, 49212, 49464, 55555, 61224, 61632, 62316, 62622, 63162, 63648, 66162, 66636, 71379, 72366, 73248, 77133, 81224, 82712, 84288, 84488, 86448, 88288, 88368, 88632, 88872, 92322, 92412, 96192, 99432, 111339, 111444, 111515, 112326, 112392, 112932, 113262, 113736, 114772, 116172, 116436, 117726, 118112, 118144, 118464, 119412, 121164, 121184, 121968, 122112, 122222, 122288, 123732, 124128, 124184, 124424, 126366, 126672, 127344, 128184, 128424, 128448, 128832, 129132, 129636, 131124, 131292, 131319, 131622, 131832, 132612, 132636, 132912, 133626, 133992, 134232, 134496, 136116, 136326, 136416, 136824, 138144, 139131, 139248, 142224, 142464, 142632, 143412, 143436, 144384, 144448, 146244, 148968, 155355, 161112, 161124, 162126, 162312, 163416, 163692, 163824, 166224, 166248, 168384, 168672, 168816, 172872, 173376, 174216, 176232, 181368, 181632, 182424, 183264, 184112, 187824, 188496, 188664, 191115, 192168, 192816, 193248, 193896, 194184, 194436, 196488, 196992, 198216, 198648, 199296, 211112, 211288, 211332, 212322, 212412, 212622, 213126, 213336, 213966, 214848, 216126, 216366, 216864, 219132, 219366, 221248, 221262, 221328, 221832, 222132, 222648, 222824, 222912, 223122, 224224, 226296, 226362, 227444, 228224, 228888, 229626, 229824, 229932, 231222, 231288, 231984, 232236, 233316, 233448, 233616, 234396, 236622, 237384, 238464, 239112, 241164, 241184, 242112, 242244, 242928, 243432, 244184, 244272, 249912, 261144.

Some larger examples :