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Duffinian n.  and  Lehmer n.

First numbers that belong to both sets:

85, 133, 247, 259, 451, 481, 511, 595, 763, 949, 1105, 1111, 1141, 1261, 1285, 1351, 1387, 1417, 1843, 2047, 2071, 2119, 2431, 2509, 2761, 3097, 3145, 3277, 3409, 3589, 3655, 3667, 4033, 4039, 4141, 4369, 4411, 4681, 4795, 5083, 5461, 5611, 5629, 5713, 6031, 6205, 6331, 7051, 7081, 7141, 7471, 7501, 7957, 8071, 8119, 8227, 8245, 8401, 8695, 8911, 8995, 9061, 9079, 9211, 9253, 9367, 9605, 9709, 9997, 10213, 10291, 10573, 10795, 10963, 11041, 11155, 11899, 13021, 13333, 13651, 13747, 13855, 13981, 14089, 14491, 14497, 14611, 14701, 14911, 14989, 15181, 15811, 15841, 16021, 16297, 16405, 16441, 16531, 16705, 16745, 16771, 16861, 17611, 17767, 18019, 18031, 18151, 18631, 18745, 18967, 19345, 19669, 19951, 20419, 21037, 21349, 21679, 21845, 21907, 22015, 22261, 23281, 23959, 24643, 24727, 24871, 25141, 25351, 25669, 26281, 26467, 26599, 26923, 27223, 27331, 27511, 27721, 28231, 28453, 28645, 28939, 29341, 30481, 30583, 30889, 31171, 31417, 31459, 31609, 31621, 32407, 32551, 33001, 33709, 34441, 34861, 35371, 35551, 35881, 36091, 36391, 36661, 36751, 36805, 37231, 37921, 37969, 39091, 39817, 40261, 40501, 40885, 40921, 41245, 41395, 41881, 42001, 42121, 42127, 42217, 42661, 42799, 43387, 43435, 43621, 44011, 45551, 45811, 45991, 46657, 47197, 47239, 47545, 47671, 47989, 48133, 48709, 49051, 49267, 49471, 49771, 49987, 50251, 50557, 50737, 50881, 52429, 52633, 52801, 53083, 53131, 53983, 54223, 54811, 55423, 55471, 55651, 55699, 55831, 55969, 56137, 56551, 56797, 57205, 59641, 61249, 62893, 63139, 63631, 64201, 64345, 64741, 64771, 65311, 65641, 66991, 67771, 68101, 68251, 69601, 69781, 70579, 71905, 72583, 72631, 73261, 73555, 73891, 74023, 74593, 75361, 76741, 76921, 77161, 78013, 78403, 79381, 80665, 80971, 81631, 81691, 82411, 83011, 83293, 83569, 83821, 84169, 85471, 85591, 86023, 86731, 88357, 88453, 88561, 88621, 90751, 90973, 92053, 92833, 92929.

Some larger examples :