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Harshad n.  and  nude n.

First numbers that belong to both sets:

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 111, 112, 126, 132, 135, 144, 162, 216, 222, 224, 264, 288, 312, 315, 324, 333, 336, 396, 432, 444, 448, 555, 612, 624, 648, 666, 735, 777, 864, 888, 936, 999, 1116, 1122, 1128, 1164, 1212, 1224, 1236, 1296, 1332, 1344, 1368, 1416, 1632, 1692, 1764, 1848, 1926, 1944, 1962, 2112, 2124, 2136, 2196, 2212, 2232, 2244, 2316, 2322, 2412, 2424, 2448, 2664, 2688, 2772, 2916, 3132, 3144, 3168, 3216, 3222, 3276, 3312, 3324, 3366, 3384, 3432, 3492, 3612, 3636, 3816, 3864, 3888, 3924, 3996, 4112, 4116, 4172, 4212, 4224, 4248, 4332, 4368, 4392, 4424, 4464, 4488, 4644, 4824, 4848, 4872, 4932, 4968, 6132, 6192, 6264, 6288, 6312, 6336, 6384, 6444, 6624, 6636, 6648, 6696, 6762, 6864, 6912, 6966, 7266, 7644, 7728, 8112, 8136, 8224, 8424, 8448, 8664, 8736, 8848, 9126, 9144, 9162, 9216, 9288, 9324, 9396, 9432, 9612, 9666, 9936, 11112, 11115, 11124, 11128, 11133, 11136, 11172, 11196, 11232, 11244, 11248, 11313, 11316, 11322, 11331, 11355, 11412, 11424, 11448, 11535, 11664, 11676, 11688, 11824, 11916, 12132, 12144, 12168, 12216, 12222, 12312, 12324, 12366, 12384, 12432, 12492, 12612, 12636, 12726, 12768, 12816, 12924, 13113, 13116, 13122, 13131, 13155, 13212, 13224, 13248, 13266, 13311, 13332, 13335, 13377, 13392, 13464, 13488, 13515, 13626, 13644, 13662, 13755, 13776, 13797, 13824, 13848, 13932, 14112, 14124, 14128, 14184, 14232, 14292, 14328, 14364, 14412, 14436, 14448, 14616, 14688, 14784, 14832, 15135, 15315, 16128, 16164, 16212, 16236, 16326, 16344, 16362, 16368, 16416, 16464, 16632, 16716, 16848, 17115, 17136, 17199, 17248, 17262, 17472, 17535, 17724, 17766, 17955, 18144, 18168, 18216, 18224, 18384, 18432, 18816, 19116, 19224, 19332, 19926, 21112, 21132, 21144, 21168, 21184, 21216.

Some larger examples :