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Harshad n.  and  unprimeable n.

First numbers that belong to both sets:

200, 204, 320, 322, 324, 510, 512, 516, 518, 624, 840, 846, 1130, 1134, 1140, 1148, 1260, 1330, 1332, 1344, 1350, 1410, 1416, 1500, 1674, 1680, 1710, 1764, 1854, 1890, 1896, 1898, 1920, 1926, 1962, 1968, 2040, 2070, 2100, 2106, 2196, 2322, 2400, 2408, 2484, 2490, 2580, 2584, 2820, 2826, 2940, 2982, 3055, 3096, 3144, 3150, 3172, 3240, 3268, 3420, 3472, 3474, 3480, 3486, 3504, 3564, 3660, 3744, 3750, 3780, 3784, 3816, 3952, 3956, 3990, 3996, 4032, 4060, 4065, 4068, 4080, 4086, 4100, 4102, 4104, 4108, 4140, 4148, 4192, 4194, 4302, 4380, 4410, 4470, 4536, 4550, 4554, 4572, 4576, 4680, 4716, 4740, 4746, 4760, 4770, 4774, 4776, 4824, 4842, 4848, 4920, 5040, 5044, 5060, 5066, 5120, 5124, 5130, 5256, 5310, 5364, 5368, 5370, 5372, 5376, 5454, 5460, 5490, 5496, 5544, 5616, 5670, 5724, 5754, 5760, 5764, 5910, 5940, 5960, 5962, 5994, 6180, 6400, 6405, 6408, 6516, 6534, 6624, 6640, 6642, 6648, 6720, 6750, 6754, 6810, 6930, 6936, 7080, 7092, 7110, 7140, 7146, 7164, 7260, 7266, 7268, 7272, 7372, 7380, 7440, 7614, 7650, 7656, 7760, 7770, 7776, 7800, 7830, 7982, 8020, 8025, 8028, 8040, 8046, 8070, 8136, 8154, 8250, 8330, 8334, 8338, 8340, 8400, 8406, 8478, 8480, 8550, 8610, 8652, 8856, 8904, 8910, 8918, 9036, 9072, 9082, 9144, 9212, 9216, 9300, 9306, 9350, 9360, 9380, 9384, 9386, 9450, 9456, 9504, 9560, 9702, 9752, 9774, 9912, 9990, 10010, 10012, 10014, 10016, 10020, 10024, 10026, 10040, 10044, 10050, 10056, 10080, 10120, 10122, 10125, 10128, 10200, 10206, 10208, 10230, 10232, 10236, 10296, 10380, 10384, 10386, 10400, 10402, 10404, 10406, 10410, 10416, 10440, 10540, 10545, 10548, 10574, 10672, 10674, 10740, 10746, 10764, 10800, 10802, 10810, 10812, 10815, 10816, 10818, 10872, 10920, 10926, 10960, 10962, 10968.

Some larger examples :