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Harshad n.  and  lucky n.

First numbers that belong to both sets:

1, 3, 7, 9, 21, 63, 111, 133, 135, 171, 195, 201, 261, 285, 399, 511, 621, 645, 735, 777, 801, 1011, 1053, 1095, 1101, 1107, 1183, 1233, 1251, 1275, 1323, 1365, 1387, 1417, 1455, 1503, 1545, 1611, 1659, 1701, 2001, 2023, 2085, 2115, 2133, 2355, 2403, 2445, 2511, 2625, 2667, 2715, 2755, 2821, 3031, 3055, 3075, 3097, 3123, 3213, 3297, 3411, 3439, 3675, 3781, 3969, 4023, 4041, 4131, 4179, 4203, 4335, 4465, 4809, 4887, 5103, 5149, 5211, 5235, 5325, 5491, 5589, 5691, 5817, 5833, 5967, 6111, 6175, 6195, 6331, 6399, 6447, 6573, 6669, 6951, 7035, 7077, 7101, 7215, 7501, 7833, 8001, 8085, 8227, 8289, 8575, 8829, 8841, 8937, 9253, 9471, 9475, 10017, 10071, 10095, 10125, 10143, 10275, 10279, 10341, 10365, 10431, 10635, 10725, 11205, 11223, 11245, 11487, 11535, 11865, 11991, 12015, 12103, 12141, 12165, 12321, 12411, 12435, 12495, 12673, 13113, 13117, 13203, 13245, 13335, 13515, 14031, 14053, 14211, 14505, 14521, 14875, 15003, 15519, 15645, 15771, 16101, 16275, 16389, 17001, 17115, 17119, 17157, 17283, 17409, 17535, 17913, 18145, 18279, 18475, 18495, 18543, 18765, 18819, 18873, 19173, 19197, 19467, 19551, 19629, 19791, 19825, 20043, 20085, 20133, 20151, 20197, 20355, 20371, 20403, 20445, 20511, 20539, 20605, 20805, 20937, 21015, 21051, 21073, 21075, 21189, 21231, 21255, 21307, 21345, 21411, 21567, 21615, 21693, 21819, 21897, 22009, 22113, 22155, 22197, 22401, 22591, 22711, 22827, 22869, 22953, 22975, 23031, 23145, 23457, 23709, 23835, 23961, 24405, 24591, 24643, 24759, 24843, 25095, 25215, 25347, 25569, 25677, 25893, 26025, 26115, 26221, 26229, 26595, 26649, 26733, 26757, 27037, 27105, 27189, 27237, 27363, 27475, 27741, 27783, 28119, 28245, 28375, 28405, 28593, 28825, 29127, 29253, 29295, 29349, 29457, 29781, 30075, 30121, 30231, 30303, 30387, 30411, 30765, 30901, 30969, 31003, 31135, 31221, 31311.

Some larger examples :