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Lehmer n.  and  lucky n.

First numbers that belong to both sets:

15, 51, 133, 259, 451, 511, 679, 1105, 1261, 1285, 1387, 1417, 2821, 3031, 3097, 3409, 3655, 4033, 5151, 5551, 5713, 6031, 6331, 6601, 7081, 7471, 7501, 8071, 8227, 8827, 8995, 9061, 9139, 9211, 9253, 9997, 10291, 10585, 12801, 13021, 13741, 14491, 16297, 16771, 17563, 17733, 17767, 18019, 18151, 18745, 18967, 21931, 24643, 24727, 26281, 26467, 26599, 26923, 27331, 27511, 29341, 31611, 32407, 35113, 35881, 36499, 36805, 37969, 38503, 39831, 39865, 40921, 41245, 41395, 42661, 43621, 45811, 45991, 47989, 48133, 49045, 49141, 49155, 49471, 49567, 51319, 52429, 54223, 55423, 55831, 56661, 56797, 57715, 64345, 65683, 72535, 75055, 79003, 79381, 83293, 83569, 85591, 88561, 90973, 92053, 92929, 93031, 94831, 96139, 101935, 104653, 105001, 107929, 108691, 113401, 113611, 114589, 115921, 116935, 124015, 124645, 125581, 125677, 126133, 127723, 129031, 130351, 131461, 133141, 134521, 138481, 141571, 142681, 143893, 146611, 146791, 147967, 148831, 149443, 151747, 153595, 156655, 161701, 167713, 171445, 172501, 176149, 184255, 184891, 189289, 197011, 198871, 200911, 204001, 206371, 210871, 213265, 216931, 219781, 220405, 224995, 226081, 227461, 227767, 228361, 230461, 240241, 245659, 247111, 249271, 250321, 261997, 267691, 269011, 270481, 271051, 274981, 275887, 278545, 279871, 280891, 281029, 285541, 287869, 288619, 289807, 293845, 298831, 301801, 304399, 309171, 309211, 311695, 312721, 319021, 325471, 325591, 331381, 332443, 333915, 335923, 340561, 341503, 345967, 346801, 350227, 355291, 367081, 369889, 371911, 374503, 375985, 375991, 382411, 383653, 385003, 387961, 393261, 397579, 406771, 407431, 410041, 416179, 420487, 423793, 425257, 432565, 440251, 443479, 443719, 455533, 455731, 457561, 458989, 459781, 464185, 468541, 475471, 483295, 488881, 494053, 497377, 513247, 514591, 518053, 520591, 520801, 521293, 521437, 522691, 530611, 531931, 537421, 538135, 543973, 545941, 546013, 553519, 559903, 561241, 561511, 562981, 568345, 568711, 573667, 575719, 577681, 580831, 585661, 585871, 594301, 597871, 601441, 610051, 613561, 614107, 617281, 617989, 625795, 628603.

Some larger examples :