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Harshad n.  and  hoax n.

First numbers that belong to both sets:

84, 234, 308, 336, 364, 476, 516, 644, 645, 660, 690, 702, 732, 735, 915, 1116, 1148, 1344, 1404, 1812, 2064, 2106, 2232, 2236, 2265, 2352, 2401, 2625, 2640, 2760, 2826, 2924, 3036, 3042, 3164, 3172, 3268, 3345, 3390, 3474, 3615, 3618, 3920, 3930, 4116, 4148, 4212, 4590, 4636, 4770, 4776, 4824, 4920, 5022, 5052, 5094, 5145, 5344, 5412, 5525, 5652, 5742, 6060, 6066, 6175, 6315, 6390, 6600, 6714, 6900, 7038, 7150, 7212, 7236, 7268, 7362, 7506, 7650, 8224, 8244, 8334, 8924, 8932, 9015, 9096, 9180, 9306, 9330, 9350, 9528, 9540, 9630, 10044, 10075, 10188, 10192, 10268, 10278, 10406, 10560, 10604, 10704, 10854, 10926, 11124, 11228, 11232, 11476, 11484, 11574, 11688, 11712, 11739, 12144, 12256, 12366, 12532, 12546, 12558, 12612, 12780, 13175, 13194, 13328, 13408, 13428, 13518, 13560, 13770, 13848, 14076, 14472, 14476, 14520, 14724, 14725, 14814, 15024, 15164, 15282, 15712, 15720, 16093, 16125, 16434, 16500, 16653, 17150, 17212, 17226, 17250, 17575, 17661, 17736, 17880, 18016, 18018, 18032, 18168, 18278, 18316, 18360, 18612, 18702, 19080, 19170, 19176, 19260, 20208, 20376, 20556, 20844, 20970, 21284, 21504, 21615, 21708, 21852, 21942, 22086, 22266, 22386, 22488, 22508, 22518, 22590, 22608, 22950, 23148, 23238, 23496, 23784, 23850, 23920, 24240, 24264, 24352, 24480, 24640, 24732, 25092, 25156, 25298, 25434, 25484, 25560, 25564, 25675, 26154, 26400, 26865, 26946, 27036, 27126, 27475, 27540, 27600, 27748, 28152, 28182, 28322, 28574, 28620, 28680, 30132, 30390, 30464, 30564, 30696, 30750, 30834, 30930, 31252, 31266, 31338, 31740, 31950, 32144, 32562, 32568, 33024, 33045, 33090, 33124, 33315, 33336, 33712, 33764, 33775, 33864, 33900, 33912, 34048, 34254, 34452, 34675, 34722, 35490, 35805, 36015, 36036, 36270, 36300, 36384, 36522, 36720, 36850, 37176, 37224, 37320, 37404, 37608, 38160, 38250, 38340, 38520, 38525, 39030, 39114, 39200.

Some larger examples :