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happy n.  and  Harshad n.

First numbers that belong to both sets:

1, 7, 10, 70, 100, 133, 190, 192, 230, 280, 320, 392, 440, 644, 700, 736, 820, 874, 888, 910, 912, 1000, 1088, 1090, 1092, 1122, 1125, 1128, 1141, 1148, 1152, 1185, 1188, 1212, 1215, 1233, 1251, 1274, 1275, 1300, 1323, 1330, 1332, 1512, 1521, 1547, 1679, 1725, 1744, 1785, 1812, 1815, 1818, 1900, 1920, 2030, 2080, 2112, 2115, 2133, 2151, 2175, 2212, 2260, 2300, 2313, 2331, 2448, 2478, 2484, 2511, 2574, 2584, 2620, 2715, 2752, 2754, 2755, 2771, 2800, 2844, 2856, 2919, 3020, 3031, 3038, 3097, 3100, 3123, 3132, 3200, 3213, 3231, 3290, 3312, 3321, 3328, 3383, 3456, 3536, 3546, 3564, 3616, 3654, 3760, 3920, 4040, 4046, 4148, 4172, 4225, 4248, 4284, 4336, 4356, 4400, 4428, 4482, 4494, 4536, 4554, 4572, 4577, 4636, 4752, 4774, 4807, 4824, 4842, 4872, 4887, 4995, 5056, 5066, 5112, 5121, 5187, 5211, 5274, 5306, 5346, 5364, 5436, 5454, 5472, 5525, 5544, 5628, 5634, 5724, 5742, 5817, 5994, 6220, 6258, 6346, 6354, 6440, 6534, 6825, 7000, 7125, 7215, 7254, 7360, 7398, 7452, 7475, 7514, 7518, 7524, 7542, 7581, 7598, 7744, 7859, 7884, 7938, 8020, 8088, 8112, 8115, 8118, 8200, 8244, 8274, 8330, 8397, 8424, 8442, 8478, 8512, 8526, 8652, 8715, 8740, 8748, 8808, 8848, 8880, 8937, 9010, 9012, 9100, 9120, 9219, 9386, 9912, 10000, 10090, 10092, 10122, 10125, 10128, 10152, 10185, 10188, 10212, 10215, 10233, 10251, 10275, 10300, 10309, 10323, 10332, 10472, 10512, 10521, 10528, 10574, 10724, 10725, 10727, 10812, 10815, 10818, 10857, 10880, 10900, 10920, 11022, 11025, 11028, 11052, 11085, 11088, 11120, 11124, 11142, 11186, 11202, 11205, 11208, 11210, 11214, 11220, 11223, 11232, 11241, 11248, 11250, 11280, 11322, 11358, 11410, 11412, 11421, 11476, 11480, 11492, 11502, 11520, 11538, 11580, 11645, 11647, 11805, 11808, 11820.

Some larger examples :