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admirable n.  and  interprime n.

First numbers that belong to both sets:

12, 30, 42, 56, 102, 120, 138, 186, 246, 270, 282, 426, 532, 582, 618, 642, 650, 822, 834, 1036, 1158, 1488, 1698, 1878, 2022, 2082, 2094, 2238, 2382, 2526, 2658, 2716, 2802, 2922, 2946, 3462, 3522, 3558, 3714, 3786, 3858, 3918, 4038, 4146, 4206, 4564, 4638, 4676, 4722, 4866, 4962, 5068, 5442, 5946, 6126, 6198, 6306, 6356, 6558, 6702, 7302, 7425, 7494, 7554, 7734, 8454, 8538, 8598, 8826, 9426, 9678, 10326, 10482, 10938, 11166, 11226, 11694, 12162, 12378, 12522, 12786, 12822, 12918, 13218, 13506, 13722, 13758, 13866, 13998, 14082, 14298, 14334, 14358, 14646, 15126, 15294, 15316, 15546, 15764, 16062, 17274, 17418, 17742, 17948, 18138, 18498, 19254, 19326, 19542, 19842, 19878, 20442, 20478, 21174, 21426, 21558, 21678, 21738, 22038, 22674, 22998, 23466, 23538, 23574, 23682, 24774, 24918, 25302, 25698, 25782, 26454, 26526, 26682, 26706, 26886, 26898, 27282, 27402, 27498, 27546, 27582, 27942, 28398, 28506, 28544, 28554, 28924, 29226, 29514, 30126, 30138, 30256, 30555, 31026, 31074, 31182, 31782, 31854, 32322, 32442, 32760, 32898, 33006, 33018, 33186, 33964, 34158, 34302, 34412, 34698, 34842, 34962, 34972, 35094, 35286, 35756, 36174, 36316, 36546, 36988, 37194, 37374, 37542, 37626, 37866, 37902, 38238, 39126, 39172, 39378, 39414, 39594, 39714, 39844, 40038, 41142, 41178, 41394, 41766, 41982, 42006, 42078, 43065, 43204, 43266, 43484, 43782, 44106, 44214, 44706, 44922, 45138, 45858, 46038, 46554, 47046, 47274, 47706, 47778, 49578, 49924, 49974, 50214, 50262, 51234, 51438, 51716, 51846, 51882, 52062, 52158, 52278, 53166, 53538, 53646, 54006, 54174, 54354, 54402, 54966, 55122, 55218, 55254, 55362, 55636, 55662, 55686, 56084, 56346, 56478, 56514, 56598, 56946, 57066, 57198, 58398, 58602, 59154, 59442, 59574, 61684, 61964, 62142, 62636, 63582, 64002, 64254, 64686, 65838, 65874, 66282, 66668, 66954, 66966, 67038, 67542, 68394, 68622, 68802, 68898.

Some larger examples :