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Duffinian n.  and  interprime n.

First numbers that belong to both sets:

4, 9, 21, 39, 50, 64, 81, 93, 111, 129, 144, 205, 217, 225, 279, 309, 324, 351, 363, 381, 399, 453, 489, 515, 625, 667, 687, 723, 741, 803, 939, 1003, 1011, 1089, 1197, 1207, 1243, 1281, 1299, 1313, 1443, 1465, 1505, 1517, 1537, 1569, 1575, 1647, 1681, 1737, 1817, 1839, 1875, 1922, 1983, 2007, 2075, 2105, 2191, 2217, 2271, 2303, 2379, 2405, 2439, 2453, 2585, 2601, 2613, 2619, 2627, 2667, 2709, 2783, 2811, 2847, 3055, 3073, 3081, 3099, 3175, 3189, 3197, 3225, 3265, 3337, 3353, 3423, 3441, 3459, 3505, 3565, 3600, 3665, 3909, 3937, 3995, 4096, 4105, 4189, 4403, 4415, 4449, 4535, 4555, 4575, 4629, 4685, 4697, 4771, 4791, 4807, 4883, 4925, 4971, 5079, 5093, 5169, 5184, 5193, 5249, 5349, 5403, 5513, 5529, 5571, 5691, 5697, 5787, 5817, 5833, 5859, 5889, 5913, 5933, 5997, 6033, 6050, 6107, 6157, 6185, 6219, 6293, 6393, 6409, 6613, 6667, 6749, 6771, 6813, 6877, 7023, 7033, 7041, 7063, 7091, 7115, 7381, 7442, 7479, 7533, 7567, 7597, 7641, 7671, 7677, 7725, 7747, 7835, 7847, 7913, 7923, 7943, 7957, 8001, 8135, 8185, 8271, 8289, 8341, 8373, 8437, 8464, 8507, 8553, 8589, 8635, 8703, 8855, 8931, 8937, 8957, 9021, 9079, 9097, 9167, 9193, 9201, 9233, 9485, 9527, 9543, 9569, 9607, 9621, 9637, 9655, 9727, 9775, 9797, 9823, 9865, 10085, 10107, 10161, 10173, 10187, 10217, 10233, 10269, 10317, 10363, 10431, 10443, 10493, 10507, 10677, 10717, 10897, 10983, 11015, 11037, 11077, 11241, 11259, 11267, 11293, 11325, 11361, 11405, 11417, 11457, 11469, 11477, 11511, 11619, 11627, 11645, 11667, 11725, 11737, 11795, 11829, 11947, 11997, 12009, 12085, 12099, 12131, 12153, 12159, 12207, 12233, 12279, 12385, 12427, 12483, 12533, 12693, 12717, 12815, 12835, 12847, 12871, 12891, 12909, 12947, 12981, 13021, 13115.

Some larger examples :