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amenable n.  and  Duffinian n.

First numbers that belong to both sets:

8, 9, 16, 21, 25, 32, 36, 49, 57, 64, 65, 77, 81, 85, 93, 100, 121, 125, 128, 129, 133, 144, 161, 169, 185, 189, 201, 205, 209, 217, 221, 225, 237, 245, 253, 256, 265, 289, 301, 305, 309, 324, 325, 329, 333, 341, 361, 365, 377, 381, 385, 392, 400, 413, 417, 425, 437, 453, 469, 481, 484, 485, 489, 493, 497, 505, 512, 513, 517, 525, 529, 533, 549, 553, 565, 576, 589, 597, 605, 625, 629, 633, 649, 657, 669, 676, 685, 689, 697, 713, 721, 729, 737, 741, 749, 777, 781, 784, 785, 793, 800, 805, 813, 817, 833, 837, 841, 845, 849, 865, 869, 873, 889, 893, 900, 901, 905, 913, 917, 921, 925, 949, 961, 965, 968, 981, 985, 989, 993, 1024, 1025, 1029, 1037, 1053, 1057, 1073, 1081, 1085, 1089, 1101, 1105, 1121, 1133, 1137, 1141, 1156, 1157, 1161, 1165, 1177, 1189, 1197, 1205, 1209, 1225, 1241, 1253, 1261, 1265, 1273, 1281, 1285, 1296, 1309, 1313, 1317, 1325, 1333, 1337, 1349, 1352, 1357, 1369, 1385, 1389, 1393, 1397, 1405, 1413, 1417, 1421, 1444, 1445, 1457, 1461, 1465, 1469, 1477, 1497, 1501, 1505, 1513, 1517, 1525, 1529, 1533, 1537, 1541, 1565, 1569, 1573, 1577, 1585, 1589, 1600, 1629, 1633, 1641, 1645, 1649, 1661, 1673, 1677, 1681, 1685, 1705, 1713, 1737, 1765, 1769, 1781, 1793, 1805, 1809, 1813, 1817, 1821, 1825, 1829, 1837, 1841, 1849, 1853, 1857, 1865, 1893, 1897, 1909, 1921, 1925, 1929, 1936, 1937, 1953, 1957, 1961, 1969, 1981, 1985, 2005, 2021, 2025, 2033, 2041, 2048, 2057, 2061, 2073, 2077, 2101, 2105, 2116, 2117, 2125, 2133, 2165, 2169, 2173, 2177, 2181, 2189, 2197, 2201, 2209, 2217, 2233, 2249, 2253, 2257, 2261.

Some larger examples :