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Harshad n.  and  untouchable n.

First numbers that belong to both sets:

2, 5, 120, 162, 210, 216, 288, 306, 322, 324, 336, 342, 372, 408, 448, 516, 518, 540, 552, 576, 612, 624, 732, 738, 756, 782, 792, 804, 902, 936, 966, 1002, 1044, 1080, 1116, 1128, 1134, 1148, 1160, 1168, 1180, 1200, 1212, 1236, 1272, 1296, 1314, 1332, 1360, 1380, 1404, 1422, 1476, 1566, 1596, 1632, 1680, 1692, 1728, 1746, 1860, 1896, 1920, 1944, 1962, 2010, 2022, 2024, 2052, 2120, 2136, 2178, 2196, 2212, 2232, 2304, 2316, 2322, 2376, 2408, 2430, 2464, 2484, 2490, 2502, 2530, 2600, 2608, 2628, 2640, 2704, 2718, 2736, 2760, 2808, 2850, 2856, 2952, 2982, 2992, 3036, 3060, 3072, 3078, 3102, 3104, 3114, 3132, 3144, 3186, 3276, 3312, 3328, 3340, 3366, 3384, 3388, 3402, 3406, 3420, 3430, 3432, 3486, 3504, 3510, 3564, 3600, 3636, 3708, 3738, 3744, 3760, 3816, 3842, 3888, 3900, 3904, 3942, 3960, 3982, 4032, 4046, 4048, 4068, 4070, 4086, 4104, 4116, 4148, 4172, 4224, 4248, 4302, 4320, 4336, 4356, 4368, 4380, 4480, 4488, 4500, 4512, 4662, 4740, 4770, 4830, 4842, 4860, 4914, 5016, 5044, 5094, 5160, 5184, 5202, 5256, 5292, 5320, 5328, 5346, 5364, 5372, 5376, 5490, 5512, 5544, 5568, 5616, 5700, 5724, 5760, 5778, 5832, 5876, 5886, 5920, 5922, 6000, 6060, 6064, 6084, 6120, 6180, 6228, 6240, 6282, 6310, 6352, 6372, 6384, 6420, 6462, 6480, 6516, 6588, 6606, 6624, 6642, 6822, 6966, 7032, 7056, 7074, 7092, 7140, 7146, 7164, 7200, 7260, 7266, 7272, 7344, 7360, 7380, 7392, 7416, 7470, 7504, 7598, 7614, 7620, 7632, 7668, 7740, 7770, 7944, 7992, 8000, 8004, 8028, 8046, 8064, 8080, 8100, 8110, 8136, 8154, 8160, 8190, 8204, 8262, 8280, 8316, 8334, 8340, 8352, 8442, 8478, 8480, 8512, 8532, 8592, 8622, 8640, 8802, 8848, 8856, 8904, 9020, 9022.

Some larger examples :