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Achilles n.  and  odious n.

First numbers that belong to both sets:

200, 392, 648, 675, 800, 968, 1125, 1568, 2312, 2592, 2700, 2888, 3200, 3872, 4232, 4500, 4563, 5000, 5400, 6272, 6728, 7688, 8575, 8712, 8748, 8788, 9000, 9248, 9800, 10368, 10800, 11552, 11907, 11979, 12168, 12800, 13448, 14792, 15488, 16928, 17496, 18000, 18252, 19208, 19773, 20000, 20808, 21600, 24200, 25088, 25947, 26912, 27848, 28125, 30752, 33275, 33800, 34300, 34848, 34992, 35152, 35912, 36000, 36504, 36992, 39200, 40328, 41067, 41472, 43200, 44217, 45000, 46208, 47432, 47628, 47916, 48668, 48672, 49928, 51200, 53792, 54675, 54925, 57800, 59168, 59643, 60552, 61952, 63368, 65219, 66248, 67228, 67712, 68600, 69984, 70227, 70304, 72000, 72200, 73008, 75272, 76832, 77175, 79092, 80000, 81608, 83232, 84375, 84872, 86400, 95256, 95832, 96800, 97556, 99127, 100352, 102152, 103788, 105125, 107163, 107648, 107653, 109503, 109512, 111392, 112500, 117128, 120125, 121203, 123008, 129032, 133100, 133128, 134456, 135200, 136107, 137200, 137288, 139392, 139968, 143648, 143883, 144000, 145800, 146016, 147968, 151875, 154568, 156800, 158184, 160083, 161312, 163592, 164268, 165888, 168200, 168507, 171475, 171500, 172800, 172872, 176868, 177608, 180000, 181447, 184832, 187272, 189728, 190125, 190512, 191664, 194672, 194688, 195075, 197192, 199712, 204800, 207576, 212552, 215168, 218700, 219501, 219700, 223112, 225000, 228488, 231200, 236672, 238572, 239432, 240737, 242208, 245000, 247808, 253125, 253472, 256328, 260876, 262088, 264992, 265837, 266200, 268912, 270848, 273800, 274400, 280908, 281216, 285768, 288000, 288463, 288800, 292032, 297675, 297992, 299475, 300125, 301088, 304175, 307328, 308700, 310472, 316368, 318028, 320000, 320787, 323208, 325125, 326432, 328536, 332667, 332928, 336091, 337500, 339488, 345600, 349448, 351125, 353736, 357075, 364500, 369800, 373527, 376712, 378125, 381024, 382347, 383328, 385875, 387200, 389344, 390224, 395307, 396508, 397832, 401408, 405000, 408483, 408608, 412232, 415152, 419528, 420175, 420500, 426888, 428652, 430592, 430612, 435125, 437400, 438012, 438048, 439400, 441800, 445568, 450000, 455877, 456968, 463347, 468512.

Some larger examples :