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amenable n.  and  self n.

First numbers that belong to both sets:

1, 5, 9, 20, 53, 64, 97, 108, 121, 132, 165, 176, 209, 233, 244, 277, 288, 312, 345, 356, 389, 400, 413, 424, 457, 468, 501, 512, 525, 536, 569, 580, 613, 637, 648, 681, 692, 716, 749, 760, 793, 804, 817, 828, 861, 872, 905, 916, 929, 940, 973, 984, 1021, 1032, 1065, 1076, 1109, 1133, 1144, 1177, 1188, 1212, 1245, 1256, 1289, 1300, 1313, 1324, 1357, 1368, 1401, 1412, 1425, 1436, 1469, 1480, 1513, 1537, 1548, 1581, 1592, 1616, 1649, 1660, 1693, 1704, 1717, 1728, 1761, 1772, 1805, 1816, 1829, 1840, 1873, 1884, 1917, 1941, 1952, 1985, 1996, 2033, 2044, 2077, 2088, 2112, 2145, 2156, 2189, 2200, 2213, 2224, 2257, 2268, 2301, 2312, 2325, 2336, 2369, 2380, 2413, 2437, 2448, 2481, 2492, 2516, 2549, 2560, 2593, 2604, 2617, 2628, 2661, 2672, 2705, 2716, 2729, 2740, 2773, 2784, 2817, 2841, 2852, 2885, 2896, 2920, 2953, 2964, 2997, 3008, 3045, 3056, 3089, 3100, 3113, 3124, 3157, 3168, 3201, 3212, 3225, 3236, 3269, 3280, 3313, 3337, 3348, 3381, 3392, 3416, 3449, 3460, 3493, 3504, 3517, 3528, 3561, 3572, 3605, 3616, 3629, 3640, 3673, 3684, 3717, 3741, 3752, 3785, 3796, 3820, 3853, 3864, 3897, 3908, 3921, 3932, 3965, 3976, 4009, 4024, 4057, 4068, 4101, 4112, 4125, 4136, 4169, 4180, 4213, 4237, 4248, 4281, 4292, 4316, 4349, 4360, 4393, 4404, 4417, 4428, 4461, 4472, 4505, 4516, 4529, 4540, 4573, 4584, 4617, 4641, 4652, 4685, 4696, 4720, 4753, 4764, 4797, 4808, 4821, 4832, 4865, 4876, 4909, 4920, 4933, 4944, 4977, 4988, 5025, 5036, 5069, 5080, 5113, 5137, 5148, 5181, 5192, 5216, 5249, 5260, 5293, 5304, 5317, 5328, 5361, 5372, 5405, 5416, 5429, 5440, 5473, 5484, 5517, 5541, 5552, 5585, 5596, 5620, 5653, 5664.

Some larger examples :