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amenable n.  and  cyclic n.

First numbers that belong to both sets:

1, 5, 13, 17, 29, 33, 37, 41, 53, 61, 65, 69, 73, 77, 85, 89, 97, 101, 109, 113, 133, 137, 141, 145, 149, 157, 161, 173, 177, 181, 185, 193, 197, 209, 213, 217, 221, 229, 233, 241, 249, 257, 265, 269, 277, 281, 293, 313, 317, 321, 329, 337, 341, 345, 349, 353, 365, 373, 377, 389, 393, 397, 401, 409, 413, 421, 433, 437, 445, 449, 457, 461, 469, 473, 481, 485, 493, 501, 509, 517, 521, 533, 537, 541, 545, 553, 557, 561, 565, 569, 573, 577, 581, 589, 593, 601, 613, 617, 629, 641, 649, 653, 661, 665, 673, 677, 681, 685, 697, 701, 705, 709, 713, 717, 721, 733, 745, 749, 753, 757, 761, 769, 773, 781, 785, 789, 793, 797, 805, 809, 817, 821, 829, 853, 857, 865, 869, 877, 881, 885, 893, 901, 913, 917, 929, 933, 937, 941, 949, 953, 957, 965, 973, 977, 985, 989, 997, 1001, 1009, 1013, 1021, 1033, 1037, 1041, 1049, 1057, 1061, 1069, 1073, 1077, 1093, 1097, 1105, 1109, 1117, 1121, 1129, 1133, 1141, 1145, 1149, 1153, 1157, 1165, 1169, 1173, 1177, 1181, 1189, 1193, 1201, 1213, 1217, 1229, 1237, 1241, 1245, 1249, 1253, 1257, 1261, 1273, 1277, 1285, 1289, 1293, 1297, 1301, 1309, 1313, 1321, 1329, 1333, 1337, 1345, 1349, 1353, 1357, 1361, 1373, 1381, 1385, 1393, 1397, 1401, 1409, 1417, 1429, 1433, 1437, 1441, 1453, 1457, 1465, 1469, 1473, 1481, 1489, 1493, 1501, 1509, 1513, 1517, 1529, 1537, 1541, 1549, 1553, 1561, 1565, 1577, 1585, 1589, 1597, 1601, 1605, 1609, 1613, 1621, 1633, 1637, 1645, 1649, 1657, 1661, 1669, 1685, 1689, 1693, 1697, 1709, 1717, 1721, 1729, 1733, 1741, 1745, 1749, 1753, 1757.

Some larger examples :