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Harshad n.  and  Ulam n.

First numbers that belong to both sets:

1, 2, 3, 4, 6, 8, 18, 36, 48, 72, 102, 114, 126, 180, 209, 243, 324, 370, 400, 402, 414, 441, 522, 605, 612, 624, 690, 720, 732, 800, 820, 864, 1020, 1032, 1035, 1101, 1125, 1164, 1230, 1296, 1308, 1360, 1387, 1404, 1431, 1602, 1770, 1812, 1836, 1853, 1900, 1944, 1968, 2010, 2034, 2090, 2112, 2115, 2156, 2178, 2445, 2464, 2484, 2511, 2574, 2584, 2618, 2628, 2660, 2916, 2919, 3031, 3038, 3070, 3290, 3390, 3456, 3525, 3549, 3610, 3696, 3762, 3930, 3952, 3960, 4040, 4148, 4150, 4155, 4260, 4294, 4368, 4392, 4404, 4470, 4536, 4600, 4624, 4644, 4734, 4800, 5052, 5184, 5274, 5382, 5550, 5616, 5814, 5856, 5875, 5880, 6024, 6156, 6310, 6352, 6354, 6420, 6552, 6804, 6936, 7038, 7104, 7170, 7300, 7322, 7368, 7434, 7500, 7581, 7749, 7776, 7820, 7884, 8096, 8126, 8250, 8316, 8338, 8370, 8424, 8512, 8514, 8856, 8964, 9015, 9054, 9093, 9120, 9162, 9240, 9252, 9702, 9724, 9963, 10002, 10090, 10107, 10110, 10134, 10220, 10242, 10305, 10413, 10503, 10520, 10540, 10545, 10584, 10740, 10850, 10872, 10994, 11016, 11085, 11280, 11300, 11600, 11625, 11647, 11688, 11713, 11715, 11952, 12033, 12060, 12250, 12294, 12438, 12504, 12570, 12600, 12614, 12705, 12768, 12873, 12900, 13032, 13044, 13240, 13264, 13328, 13330, 13401, 13408, 13440, 13572, 13650, 13689, 13692, 13848, 13975, 14190, 14320, 14325, 14364, 14410, 14454, 14476, 14520, 14760, 14769, 14796, 14904, 15138, 15280, 15400, 15424, 15466, 15512, 15600, 15642, 15732, 15962, 15984, 16030, 16338, 16653, 16722, 16812, 17115, 17430, 17604, 18278, 18432, 18684, 18921, 19312, 19314, 19375, 19512, 19600, 19620, 19629, 19656, 19683, 20052, 20172, 20260, 20421, 20646, 20670, 20736, 20805, 20937, 21000, 21015, 21105, 21108, 21110, 21132, 21345, 21411, 21430, 21540, 21560, 21582, 21736, 21750, 21870, 21904.

Some larger examples :