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Smith n.  and  Zumkeller n.

First numbers that belong to both sets:

378, 438, 588, 636, 654, 666, 690, 728, 762, 852, 1086, 1284, 1376, 1626, 1736, 1776, 1842, 1872, 1908, 1952, 2484, 2556, 2576, 2688, 2944, 2958, 2964, 2970, 3138, 3168, 3174, 3246, 3294, 3366, 3390, 3564, 3690, 3864, 3930, 4428, 4464, 4472, 4592, 4788, 4794, 4880, 4960, 4974, 5088, 5172, 5248, 5298, 5388, 5772, 5874, 5936, 5946, 6036, 6054, 6096, 6188, 6252, 6344, 6684, 6702, 6760, 6816, 6880, 7026, 7062, 7068, 7674, 7764, 7782, 7784, 7824, 7952, 8154, 8196, 8372, 8412, 8466, 8568, 8628, 8680, 8736, 8754, 8790, 8792, 8874, 9184, 9276, 9294, 9296, 9330, 9396, 9648, 9708, 9760, 9840, 9880, 9924, 9942, 9968, 10086, 10296, 10494, 10698, 10736, 10806, 11388, 11696, 11790, 11816, 11984, 12318, 12558, 12648, 12656, 12684, 12732, 13506, 13662, 13764, 13812, 13974, 13984, 14046, 14058, 14148, 14168, 14464, 14508, 14672, 14688, 14736, 14756, 14784, 14832, 14924, 14946, 14958, 15018, 15126, 15558, 15704, 15824, 15848, 15860, 15882, 15884, 15984, 16098, 16192, 16480, 16536, 16592, 16688, 16744, 16746, 16770, 16890, 16902, 16940, 17056, 17238, 17268, 17496, 17646, 17664, 17718, 17754, 17826, 17840, 17864, 17916, 17940, 17982, 18132, 18396, 18474, 18618, 18732, 18846, 18872, 18920, 19212, 19272, 19280, 19292, 19360, 19376, 19428, 19482, 19554, 19590, 19644, 19812, 19818, 19880, 19952, 20784, 20888, 21066, 21186, 21498, 21896, 22188, 22368, 22386, 22448, 22734, 22816, 22884, 23192, 23484, 23658, 23694, 23736, 23790, 23870, 24096, 24306, 24354, 24552, 24678, 24828, 24928, 24954, 25064, 25256, 25392, 25398, 25428, 25844, 25928, 26096, 26292, 26394, 26480, 26660, 26676, 26682, 26760, 26768, 26826, 26840, 26892, 27156, 27270, 27280, 27468, 27546, 27666, 27696, 27756, 27768, 27792, 27804, 27846, 27950, 28068, 28182, 28208, 28236, 28280, 28284, 28336, 28380, 28392, 28662, 28716, 28784, 28808, 28840, 28920, 28952, 28960, 28980, 29166.

Some larger examples :