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nude n.  and  powerful n.

First numbers that belong to both sets:

1, 4, 8, 9, 36, 128, 144, 216, 288, 324, 432, 648, 784, 864, 1296, 1444, 1764, 1944, 2744, 2888, 2916, 3888, 6912, 9216, 11664, 12168, 12996, 13824, 14112, 18432, 21168, 23328, 24336, 24696, 26136, 26244, 28224, 31212, 34848, 34992, 36864, 41616, 42336, 49392, 62424, 69192, 69696, 69984, 77175, 82944, 83232, 84672, 93312, 93636, 98784, 111132, 112896, 114244, 114264, 116964, 124416, 124848, 133128, 138384, 139392, 139968, 148176, 166464, 169344, 172872, 186624, 191664, 194688, 199692, 213444, 221184, 222264, 228488, 233928, 236196, 246924, 248832, 249696, 294912, 311364, 313632, 314928, 316368, 332928, 333396, 338688, 363312, 383328, 383688, 399384, 412164, 426888, 431244, 442368, 484128, 484416, 493848, 499392, 636192, 646416, 666792, 677376, 691488, 777924, 824328, 862488, 914112, 919368, 968832, 969624, 1123632, 1149984, 1161288, 1168128, 1182816, 1192464, 1213488, 1218816, 1236492, 1241888, 1281424, 1292832, 1313316, 1314144, 1382976, 1391112, 1411344, 1414944, 1431432, 1468944, 1492992, 1633932, 1663488, 1722448, 1778112, 1788696, 1828224, 1866312, 1868184, 1912968, 1939248, 2122416, 2143296, 2196324, 2214144, 2222316, 2239488, 2281248, 2286144, 2299968, 2333772, 2384928, 2414916, 2626632, 2628288, 2661336, 2663424, 2667168, 2681928, 2696112, 2822688, 2829888, 2862864, 2988216, 3111696, 3183624, 3196944, 3214944, 3232332, 3261636, 3283344, 3321216, 3392964, 3429216, 3483864, 3612672, 3663396, 3732624, 3841992, 3942432, 3944196, 3981312, 4148928, 4173624, 4181832, 4244832, 4294296, 4392648, 4416984, 4428288, 4444632, 4741632, 4822416, 4829832, 4942368, 4962312, 4981824, 6133248, 6181128, 6223392, 6322176, 6324912, 6393888, 6429888, 6441444, 6464664, 6642432, 6963912, 7112448, 7137144, 7641648, 7683984, 8347248, 8363664, 8433216, 8489664, 8669448, 8813664, 8821888, 8833968, 8889264, 8928144, 8964648, 9124992, 9176328, 9326916, 9383112, 9483264, 9644832, 9696996, 9891936, 9924624, 9963648, 11128896, 11142244, 11197872, 11214848, 11249316, 11389248, 11462472, 11614464, 11693448, 11861136, 11868192, 11943936, 12122888, 12162312, 12192768, 12266496, 12338136, 12446784, 12632112, 12649824, 12882888, 12929328, 13127688, 13189248, 13264164, 13284864, 13333896, 13381632, 13392216, 13395375, 13436928, 13446972, 13686912, 13716864, 13764492, 13972644, 14129928, 14224896, 14274288, 14386248, 14489496, 14886936.

Some larger examples :