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amenable n.  and  lucky n.

First numbers that belong to both sets:

1, 9, 13, 21, 25, 33, 37, 49, 69, 73, 93, 105, 129, 133, 141, 169, 189, 193, 201, 205, 237, 241, 261, 273, 285, 289, 297, 321, 349, 357, 361, 385, 393, 409, 421, 429, 433, 477, 489, 517, 529, 537, 541, 553, 577, 601, 613, 621, 645, 673, 685, 693, 717, 729, 741, 745, 769, 777, 781, 801, 805, 841, 873, 885, 897, 925, 933, 937, 957, 961, 981, 993, 997, 1009, 1021, 1029, 1041, 1053, 1057, 1093, 1101, 1105, 1117, 1189, 1197, 1201, 1209, 1233, 1245, 1249, 1261, 1281, 1285, 1309, 1329, 1357, 1365, 1369, 1389, 1401, 1417, 1441, 1473, 1485, 1497, 1501, 1533, 1545, 1585, 1597, 1641, 1645, 1693, 1701, 1705, 1737, 1749, 1765, 1773, 1777, 1797, 1801, 1809, 1833, 1857, 1869, 1893, 1921, 1933, 1941, 1945, 1965, 1977, 2001, 2053, 2065, 2085, 2113, 2121, 2125, 2133, 2173, 2209, 2217, 2221, 2253, 2257, 2277, 2281, 2301, 2317, 2365, 2409, 2445, 2461, 2473, 2493, 2505, 2545, 2557, 2589, 2593, 2625, 2649, 2653, 2661, 2689, 2697, 2725, 2773, 2781, 2785, 2797, 2817, 2821, 2841, 2845, 2877, 2901, 2905, 2913, 2953, 2961, 2973, 2977, 3037, 3049, 3073, 3097, 3109, 3121, 3133, 3153, 3213, 3229, 3261, 3289, 3297, 3301, 3313, 3325, 3381, 3405, 3409, 3433, 3453, 3465, 3477, 3481, 3489, 3565, 3597, 3613, 3621, 3625, 3633, 3661, 3669, 3685, 3697, 3709, 3717, 3721, 3753, 3781, 3789, 3793, 3849, 3865, 3873, 3889, 3897, 3909, 3969, 3981, 4033, 4041, 4045, 4069, 4081, 4105, 4129, 4161, 4165, 4173, 4189, 4201, 4237, 4257, 4269, 4285, 4321, 4329, 4377, 4389, 4413, 4441, 4461, 4465, 4485, 4509, 4521, 4561, 4569, 4573, 4609, 4621, 4629, 4645, 4653, 4713, 4717, 4725, 4741, 4761, 4773, 4797, 4801, 4809, 4813.

Some larger examples :