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untouchable n.  and  Zumkeller n.

First numbers that belong to both sets:

88, 96, 120, 210, 216, 246, 276, 304, 306, 336, 342, 372, 408, 426, 448, 474, 498, 516, 520, 540, 552, 612, 624, 708, 714, 726, 732, 750, 756, 768, 792, 804, 836, 852, 894, 896, 936, 966, 996, 1002, 1044, 1060, 1068, 1074, 1080, 1116, 1128, 1134, 1146, 1148, 1160, 1180, 1200, 1212, 1236, 1248, 1254, 1266, 1272, 1288, 1312, 1316, 1326, 1332, 1360, 1380, 1398, 1404, 1420, 1476, 1506, 1542, 1566, 1578, 1596, 1632, 1650, 1680, 1692, 1716, 1728, 1758, 1776, 1806, 1820, 1830, 1840, 1842, 1860, 1866, 1884, 1888, 1896, 1920, 1944, 1956, 1960, 1986, 1992, 2010, 2022, 2024, 2052, 2058, 2118, 2120, 2128, 2136, 2148, 2190, 2196, 2212, 2226, 2232, 2262, 2316, 2322, 2324, 2364, 2376, 2388, 2408, 2430, 2432, 2436, 2454, 2464, 2484, 2490, 2496, 2514, 2530, 2568, 2576, 2586, 2590, 2600, 2628, 2640, 2724, 2736, 2748, 2760, 2766, 2784, 2808, 2828, 2850, 2856, 2874, 2922, 2944, 2946, 2952, 2968, 2982, 2992, 2994, 2996, 3008, 3018, 3036, 3060, 3072, 3078, 3102, 3126, 3132, 3144, 3156, 3162, 3174, 3186, 3198, 3228, 3234, 3246, 3270, 3276, 3306, 3312, 3318, 3328, 3340, 3366, 3378, 3384, 3388, 3396, 3400, 3402, 3420, 3430, 3432, 3486, 3504, 3510, 3556, 3564, 3576, 3580, 3588, 3630, 3642, 3648, 3666, 3684, 3738, 3744, 3752, 3760, 3774, 3786, 3792, 3808, 3816, 3820, 3828, 3860, 3876, 3888, 3900, 3904, 3936, 3940, 3942, 3954, 3960, 3972, 4026, 4032, 4048, 4056, 4062, 4070, 4088, 4098, 4104, 4116, 4120, 4170, 4172, 4188, 4206, 4216, 4224, 4248, 4280, 4296, 4308, 4312, 4320, 4344, 4368, 4380, 4386, 4396, 4416, 4472, 4476, 4480, 4488, 4500, 4506, 4512, 4530, 4580, 4614, 4648, 4662, 4668, 4672, 4686, 4690, 4700, 4710, 4712, 4740, 4758, 4764.

Some larger examples :