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balanced n.  and  interprime n.

First numbers that belong to both sets:

9, 12, 15, 21, 42, 50, 56, 99, 108, 120, 150, 154, 165, 170, 180, 195, 198, 225, 228, 240, 260, 266, 312, 348, 420, 426, 462, 532, 544, 552, 566, 570, 574, 582, 590, 596, 600, 604, 618, 625, 660, 675, 696, 714, 803, 810, 944, 1190, 1294, 1922, 2014, 2022, 2134, 2139, 2142, 2157, 2170, 2191, 2205, 2229, 2247, 2259, 2268, 2277, 2284, 2290, 2349, 2364, 2379, 2382, 2386, 2396, 2405, 2420, 2430, 2439, 2453, 2470, 2613, 2652, 2661, 2674, 2680, 2709, 2716, 2730, 2772, 2790, 2826, 2835, 2854, 2883, 2892, 2900, 2913, 3099, 3129, 3150, 3213, 3219, 3225, 3252, 3300, 3304, 3353, 3366, 3372, 3410, 3459, 3462, 3465, 3468, 3480, 3522, 3528, 3536, 3552, 3610, 3634, 3640, 3651, 3665, 3672, 3684, 3730, 3736, 3849, 3852, 3858, 7041, 7091, 7115, 7503, 7755, 7835, 7881, 7913, 7943, 7957, 8001, 8135, 8169, 8175, 8323, 8382, 8430, 8437, 8445, 8507, 8541, 8553, 8666, 8679, 8696, 8703, 8813, 8826, 8855, 8862, 8877, 8890, 8931, 8937, 8946, 8957, 8985, 9035, 9046, 9130, 9144, 9177, 9339, 9374, 9450, 9543, 9549, 9607, 9621, 9626, 9637, 9669, 9684, 9758, 9814, 9836, 9877, 9894, 9926, 9930, 10023, 10068, 10096, 10122, 10136, 10146, 10179, 10281, 10295, 10302, 10350, 10395, 10413, 10428, 10431, 10443, 10458, 10470, 10482, 10521, 10545, 10604, 10610, 10629, 10635, 10645, 10665, 10700, 10736, 10842, 10860, 10906, 10953, 11015, 11052, 11058, 11064, 11077, 11085, 11090, 11154, 11160, 11172, 11247, 11267, 11283, 11293, 11319, 11361, 11405, 11417, 11430, 11469, 11490, 11523, 11565, 11590, 11595, 11619, 11725, 11737, 11795, 11804, 11817, 11832, 11916, 11940, 11970, 11976, 11984, 12042, 12072, 12104, 12162, 12207, 12233, 12285, 12375, 12405, 12427, 12435, 12476, 12489, 12494, 12507, 12522, 12573, 12595, 12650, 12665, 12693.

Some larger examples :