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Achilles n.  and  junction n.

First numbers that belong to both sets:

5324, 14112, 16928, 28125, 31212, 49928, 55125, 62424, 65219, 66125, 78732, 95832, 99127, 122825, 123008, 136125, 190125, 202612, 223112, 231525, 233523, 235224, 239432, 253125, 256328, 265837, 268119, 292032, 309123, 325125, 378125, 381024, 390224, 406125, 435125, 463736, 492032, 508032, 552123, 561125, 575532, 596232, 599427, 613832, 666125, 674028, 700928, 703125, 729632, 739328, 741125, 798848, 820125, 821516, 855432, 865928, 903125, 957728, 985527, 990125, 995328, 1005723, 1081125, 1105425, 1128125, 1131008, 1149128, 1225125, 1257728, 1267232, 1292832, 1293732, 1305728, 1326125, 1373125, 1417928, 1458632, 1485125, 1539727, 1540125, 1586032, 1605632, 1633023, 1633932, 1634432, 1648928, 1711125, 1723025, 1741932, 1774728, 1797228, 1826132, 1830125, 1835528, 1984032, 2016032, 2056223, 2080125, 2145125, 2166633, 2171528, 2238728, 2249728, 2250423, 2365632, 2382032, 2384732, 2384928, 2392533, 2415125, 2437632, 2461019, 2478843, 2495232, 2499848, 2536828, 2539732, 2556125, 2626632, 2628125, 2676429, 2681928, 2691325, 2701125, 2841728, 2860832, 2899232, 2906631, 3012012, 3024819, 3081125, 3105032, 3145032, 3158028, 3160125, 3165128, 3195731, 3288627, 3338528, 3343221, 3359232, 3377129, 3383532, 3403125, 3441123, 3461931, 3498943, 3538944, 3623432, 3688328, 3737628, 3756536, 3875328, 3895843, 3942432, 4010112, 4095125, 4131833, 4148928, 4170123, 4174016, 4181832, 4228232, 4234032, 4244832, 4298427, 4324419, 4385043, 4406832, 4444632, 4452128, 4457628, 4476032, 4494528, 4524032, 4548128, 4599936, 4667544, 4694048, 4695327, 4755528, 4775932, 4851125, 4854728, 4899852, 4950125, 5050125, 5068928, 5087327, 5094432, 5151125, 5174928, 5274828, 5370732, 5392328, 5394843, 5418632, 5491827, 5565132, 5598936, 5663628, 5725728, 5797836, 5807232, 5839036, 5926527, 5999648, 6018425, 6024024, 6069128, 6097032, 6105125, 6153032, 6344128, 6344936, 6451232, 6535728, 6537728, 6588344, 6642432, 6669243, 6777027, 6815432, 6843744, 6903125, 6904328, 6978848, 7021125, 7024032, 7140125, 7198048, 7250432, 7280928, 7294032, 7393644, 7573832, 7614943, 7636232, 7856648, 7931628, 7936128, 7968032, 8032032, 8049132, 8078643, 8137827, 8193532, 8197227, 8256843, 8258048, 8339441, 8339528, 8372232, 8382744, 8385125, 8406828, 8437832, 8470728, 8646125, 8853632, 8895852, 8949644, 8957952, 9045125, 9176328, 9180125, 9210632, 9462528, 9570132, 9591125, 9623043, 9715232, 9750528, 9752427, 9817443, 9834543, 9839048, 9850032, 9870125, 9891936.

Some larger examples :