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Achilles n.  and  Harshad n.

First numbers that belong to both sets:

72, 108, 200, 288, 392, 432, 500, 648, 800, 864, 972, 1125, 1152, 1323, 1800, 1944, 2000, 2312, 2592, 2700, 3200, 3456, 3528, 3888, 4000, 4500, 4608, 5000, 5292, 5400, 6912, 7200, 8575, 8712, 8748, 9000, 9747, 10125, 10368, 10584, 10800, 12168, 12348, 13068, 13500, 14112, 15552, 16200, 16875, 17496, 18000, 18252, 18432, 20000, 20808, 21168, 21600, 23328, 24200, 24300, 25947, 26136, 27648, 27783, 28800, 31104, 31212, 31752, 32000, 34300, 34992, 35152, 36000, 36125, 36504, 36963, 37044, 38988, 39200, 40500, 41472, 42336, 42592, 43200, 45000, 45387, 47628, 48600, 49923, 50000, 51200, 52272, 52488, 54000, 54675, 54925, 55296, 57132, 57800, 59643, 60500, 60552, 62208, 62424, 64800, 64827, 66248, 67500, 67712, 68600, 69984, 72000, 73008, 75843, 77976, 78408, 78732, 80000, 81000, 81675, 83232, 83349, 84375, 84672, 86400, 87723, 88200, 90828, 93312, 95256, 97200, 98568, 98784, 103788, 104544, 108000, 109512, 111132, 112500, 114264, 115200, 117612, 121000, 121032, 121203, 121500, 123823, 124416, 124848, 127008, 128547, 132300, 133128, 135000, 139968, 141512, 143748, 143883, 144000, 145800, 146016, 147852, 148176, 151875, 152352, 155952, 156800, 162000, 163592, 164268, 165375, 165888, 168507, 169344, 171475, 171500, 172800, 176868, 180000, 181548, 181656, 187272, 190512, 194400, 194688, 195075, 196000, 197568, 199692, 200000, 202248, 207576, 209088, 209952, 213867, 217800, 218700, 219488, 220500, 221184, 222264, 223587, 225000, 228528, 231200, 231868, 233928, 235224, 237276, 238572, 242000, 242208, 243000, 243675, 249696, 250632, 259200, 259308, 264600, 264627, 264992, 268912, 270000, 273375, 273800, 275427, 276768, 280908, 285768, 286443, 288000, 292032, 295704, 296352, 303372, 304200, 308700, 311904, 313632, 314928, 320000, 320787, 323208, 324000, 326700, 328536, 329672, 332024, 332667, 333396, 337500, 338688, 342792, 344763, 345600, 350892, 351232, 352800, 357075, 361000, 363096, 363312, 364500, 366368, 369603, 375948, 381024, 382347, 383688, 387200, 388800, 392000, 395307, 399384, 400000, 401868, 405000, 408375, 408483, 415152.

Some larger examples :