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Duffinian n.  and  Harshad n.

First numbers that belong to both sets:

4, 8, 9, 21, 27, 36, 50, 63, 81, 100, 111, 133, 144, 171, 201, 209, 225, 243, 247, 324, 333, 351, 392, 399, 400, 407, 481, 511, 512, 513, 576, 603, 605, 629, 711, 715, 777, 800, 803, 900, 935, 999, 1011, 1053, 1101, 1141, 1143, 1161, 1183, 1251, 1296, 1387, 1413, 1417, 1651, 1659, 1679, 1853, 2007, 2023, 2025, 2061, 2119, 2133, 2159, 2289, 2304, 2312, 2331, 2401, 2511, 2601, 2667, 2704, 2771, 2916, 2997, 3033, 3055, 3077, 3097, 3141, 3297, 3303, 3383, 3411, 3439, 3523, 3600, 3749, 3781, 4113, 4179, 4221, 4225, 4356, 4401, 4577, 4624, 4802, 4807, 4809, 4887, 4913, 4991, 5103, 5149, 5161, 5184, 5211, 5219, 5301, 5491, 5525, 5691, 5697, 5817, 5819, 5831, 5833, 5859, 5875, 5943, 6021, 6050, 6069, 6137, 6331, 6399, 6400, 6443, 6517, 6573, 6647, 6669, 6775, 6951, 6993, 7033, 7055, 7077, 7361, 7475, 7479, 7501, 7543, 7675, 7707, 7744, 7833, 7857, 7859, 8001, 8100, 8203, 8227, 8289, 8337, 8717, 8829, 8841, 8911, 8937, 8959, 8991, 9099, 9216, 9219, 9253, 9477, 9503, 9545, 9723, 9909, 9925, 9947, 10000, 10053, 10071, 10107, 10109, 10161, 10213, 10233, 10279, 10307, 10323, 10404, 10431, 10479, 10505, 10543, 10727, 10787, 10816, 10901, 10963, 10983, 11001, 11043, 11133, 11221, 11241, 11245, 11339, 11487, 11511, 11645, 11647, 11664, 11713, 11991, 12100, 12181, 12231, 12257, 12369, 12415, 12501, 12563, 12673, 12747, 12857, 12873, 12987, 13023, 13111, 13117, 13131, 13203, 13351, 13401, 13481, 13685, 13797, 13881, 13975, 14053, 14093, 14099, 14103, 14121, 14211, 14383, 14400, 14705, 14769, 14875, 14927, 15001, 15021, 15067, 15223, 15317, 15393, 15409, 15519, 15579, 15623, 15689, 15751, 15771, 15775, 16101, 16235, 16389, 16527, 16583, 17119, 17153, 17157, 17283, 17409, 17424, 17461, 17577, 17661, 17739, 17777, 17803.

Some larger examples :