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Harshad n.  and  Smith n.

First numbers that belong to both sets:

4, 27, 378, 576, 588, 645, 648, 666, 690, 825, 915, 1872, 1908, 1962, 2265, 2286, 2484, 2556, 2688, 2934, 2970, 3168, 3258, 3294, 3345, 3366, 3390, 3564, 3615, 3690, 3852, 3864, 3930, 4428, 4464, 4557, 4880, 5526, 6084, 6315, 7695, 8154, 8736, 8883, 9015, 9036, 9330, 9386, 9396, 9414, 9522, 9639, 10296, 10494, 11358, 11739, 11790, 12558, 12684, 13662, 14058, 14148, 14508, 14688, 14784, 14832, 14958, 14985, 15516, 15687, 15860, 15984, 16653, 16902, 16940, 16983, 17199, 17424, 17496, 17664, 17840, 17982, 18108, 18162, 18278, 18732, 18765, 18846, 18920, 19134, 19280, 19602, 19683, 19818, 20754, 21078, 21186, 21615, 22386, 22734, 24354, 24552, 24678, 25236, 25298, 25614, 25893, 26292, 26480, 26660, 26676, 26840, 26892, 27189, 27270, 27756, 27804, 28182, 28280, 28336, 28392, 28574, 28808, 28809, 29484, 29538, 29540, 29565, 29624, 29760, 30258, 30384, 30390, 30906, 30930, 31488, 32418, 32454, 32697, 32724, 32786, 33045, 33090, 33315, 33462, 33669, 33680, 33880, 34182, 34776, 35364, 35397, 35478, 35594, 35775, 35805, 36090, 36099, 36296, 36306, 36990, 37098, 37476, 37820, 37840, 38168, 38286, 39030, 39258, 39260, 39560, 39711, 40518, 41436, 41678, 42138, 43308, 44028, 44388, 44928, 45054, 45188, 45495, 45656, 45792, 45846, 46134, 46575, 47088, 47385, 47528, 47656, 47736, 47740, 47763, 47925, 48048, 48080, 48204, 48654, 49383, 49491, 49680, 49707, 49880, 49910, 50484, 50787, 51315, 51678, 51948, 52248, 52299, 52785, 52808, 52947, 52974, 53382, 53664, 53680, 53846, 54234, 54567, 54594, 54864, 54891, 54972, 55484, 55728, 55890, 56862, 56980, 57408, 57726, 58058, 58293, 58374, 58590, 58617, 59616, 59913, 60045, 60090, 60315, 60642, 60669, 61884, 61992, 62115, 62660, 62694, 62738, 62972, 63015, 63099, 63330, 63674, 64376, 64844, 65178, 65502, 65880, 65967, 66258, 66440, 66584, 66636, 66717, 66825, 66990, 67068, 67122, 67446, 67704, 68640, 68931, 69216, 69524, 69741, 70362.

Some larger examples :