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nude n.  and  square n.

First numbers that belong to both sets:

1, 4, 9, 36, 144, 324, 784, 1296, 1444, 1764, 2916, 9216, 11664, 12996, 24336, 26244, 28224, 36864, 41616, 69696, 82944, 93636, 112896, 114244, 116964, 138384, 166464, 186624, 213444, 236196, 311364, 412164, 484416, 646416, 777924, 1192464, 1218816, 1281424, 1313316, 1382976, 1411344, 1468944, 2143296, 2196324, 2214144, 2286144, 2414916, 2663424, 2862864, 3111696, 3196944, 3261636, 3283344, 3392964, 3663396, 3732624, 3944196, 4822416, 4981824, 6441444, 7683984, 8363664, 8433216, 8928144, 9326916, 9696996, 11128896, 11142244, 11249316, 11614464, 11861136, 11943936, 12446784, 13264164, 13972644, 16112196, 16842816, 18249984, 19236996, 19289664, 21123216, 21233664, 21734244, 22127616, 22924944, 23213124, 23386896, 23444964, 23736384, 24147396, 24324624, 24443136, 24621444, 26193924, 26998416, 27123264, 28132416, 31674384, 32421636, 32626944, 34433424, 34644996, 36144144, 36216324, 36433296, 36869184, 38489616, 39614436, 39841344, 41139396, 41293476, 43639236, 44116164, 44836416, 46131264, 46294416, 49196196, 49787136, 61121124, 61496964, 61968384, 62346816, 62631396, 62916624, 63393444, 64931364, 66194496, 66292164, 71267364, 72692676, 76317696, 79281216, 81216144, 81649296, 83393424, 83832336, 84492864, 86266944, 86936976, 88284816, 88962624, 89189136, 91126116, 91699776, 96118416, 98247744, 111133764, 114318864, 116899344, 117418896, 118984464, 122943744, 123343236, 124144164, 126292644, 128414224, 131194116, 133263936, 133818624, 134374464, 136328976, 136469124, 139428864, 139996224, 141276996, 141419664, 142277184, 144288144, 144432324, 146313216, 148644864, 161188416, 161493264, 163942416, 169364196, 171714816, 173923344, 178382736, 181926144, 183223296, 184199184, 186486336, 186814224, 189778176, 191434896, 191933316, 192432384, 193432464, 196784784, 199826496, 199996164, 212226624, 212926464, 216266436, 216442944, 218211984, 218921616, 219988224, 222129216, 223921296, 226622916, 231161616, 231891984, 232989696, 233722944, 234641124, 236298384, 238146624, 238887936, 243921924, 244484496, 246364416, 246741264, 248629824, 249387264, 262634436, 262828944, 276623424, 281836944, 282643344, 284664384, 286692624, 293642496, 296941824, 297976644, 298183824, 299428416, 317124864, 321413184, 324432144, 338412816, 344399364, 346629924, 349989264, 363131136, 364962816, 379782144, 389193984, 393466896, 394896384, 396328464, 398241936, 414692496, 416649744, 428986944, 429981696, 433972224, 434222244, 436224996, 439237764, 439489296, 468116496, 471497796, 486996624, 489648384, 491242896, 491774976, 494439696.