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Friedman n.  and  Harshad n.

First numbers that belong to both sets:

126, 153, 216, 736, 1206, 1260, 1296, 1503, 1530, 2502, 2592, 2916, 3784, 3864, 4536, 4624, 5120, 5832, 9216, 10192, 10251, 10368, 10426, 10521, 11025, 11664, 11844, 12006, 12060, 12100, 12102, 12103, 12104, 12105, 12108, 12321, 12384, 12544, 12546, 12600, 12762, 12768, 12798, 12960, 13176, 13689, 13824, 13842, 13950, 14256, 15003, 15030, 15246, 15300, 15552, 15623, 15624, 15642, 15645, 15689, 15795, 16272, 16368, 16794, 16875, 17346, 18270, 18432, 18522, 18744, 19026, 19392, 19629, 19682, 19683, 19684, 19737, 19845, 20736, 21504, 21870, 23328, 23490, 24336, 24339, 24390, 24576, 25725, 25872, 26244, 26973, 27648, 27783, 28224, 28322, 28674, 28728, 29160, 29184, 29524, 31252, 31590, 32697, 32778, 32781, 32786, 32832, 32851, 32859, 32875, 33696, 34992, 35152, 35937, 36850, 36855, 37179, 37449, 37840, 38637, 38640, 39366, 39424, 41472, 42336, 43932, 45360, 45364, 45684, 45760, 45873, 45927, 46608, 46640, 46641, 46648, 46656, 46688, 49896, 49968, 51200, 51759, 52488, 52947, 53865, 54378, 54432, 54642, 55296, 56295, 57645, 58978, 59049, 59052, 59064, 59265, 59319, 61440, 64512, 66339, 67149, 67392, 69255, 69822, 69984, 71199, 72576, 73926, 74358, 78165, 78732, 81648, 81920, 82755, 82936, 82944, 84375, 84672, 85293, 86142, 86724, 91854, 92160, 93312, 98304, 98415, 99225, 102051, 102384, 102505, 102510, 102528, 102784, 102942, 103680, 103688, 103824, 104026, 104260, 104328, 104329, 104368, 104858, 104895, 104916, 104976, 105021, 105210, 105264, 105624, 105750, 107649, 108126, 108216, 108612, 108864, 109350, 109375, 110250, 111132, 112536, 112590, 113724, 114246, 114268, 114352, 114390, 114576, 114681, 114688, 114696, 115248, 116478, 116640, 116937, 117369, 117396, 117475, 117630, 117634, 117639, 117642, 117666, 117728, 117747, 117936, 118272, 118440, 119430, 120006, 120060, 120384, 120600, 120762, 121086, 121203, 121536, 123084, 123354, 123648, 123768, 123840, 124362, 124368, 124416, 124542, 124632, 124659, 124956, 125000, 125001, 125004, 125006, 125008, 125010, 125018, 125020, 125025, 125028, 125040.

Some larger examples :