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amenable n.  and  Smith n.

First numbers that belong to both sets:

85, 121, 265, 517, 576, 588, 636, 645, 648, 728, 729, 825, 852, 861, 913, 985, 1165, 1284, 1376, 1449, 1581, 1633, 1736, 1776, 1872, 1881, 1908, 1921, 1952, 2173, 2265, 2373, 2409, 2461, 2484, 2556, 2576, 2605, 2688, 2745, 2785, 2888, 2944, 2964, 2965, 3168, 3345, 3505, 3564, 3649, 3852, 3864, 3865, 3973, 4173, 4185, 4189, 4209, 4369, 4428, 4464, 4472, 4557, 4592, 4765, 4788, 4832, 4880, 4960, 4981, 5088, 5172, 5248, 5253, 5269, 5305, 5388, 5397, 5485, 5772, 5936, 6036, 6084, 6096, 6188, 6252, 6344, 6385, 6457, 6585, 6684, 6693, 6760, 6816, 6880, 6981, 7068, 7089, 7136, 7249, 7465, 7712, 7764, 7784, 7809, 7824, 7952, 8005, 8073, 8077, 8149, 8185, 8196, 8253, 8257, 8277, 8372, 8412, 8421, 8545, 8568, 8628, 8653, 8680, 8736, 8792, 8864, 8901, 9036, 9184, 9193, 9229, 9276, 9285, 9296, 9301, 9396, 9633, 9648, 9657, 9684, 9708, 9717, 9760, 9840, 9849, 9861, 9880, 9924, 9968, 9985, 10201, 10296, 10489, 10592, 10664, 10669, 10689, 10705, 10736, 10761, 10797, 10845, 11065, 11209, 11385, 11388, 11696, 11785, 11816, 11857, 11965, 11984, 12573, 12648, 12656, 12684, 12732, 12937, 12957, 13369, 13472, 13764, 13765, 13812, 13905, 13984, 14017, 14085, 14148, 14168, 14464, 14508, 14672, 14688, 14736, 14756, 14784, 14809, 14832, 14881, 14924, 14985, 15128, 15205, 15369, 15516, 15529, 15704, 15709, 15824, 15848, 15853, 15860, 15884, 15981, 15984, 16105, 16137, 16192, 16269, 16285, 16357, 16480, 16536, 16537, 16568, 16592, 16645, 16653, 16688, 16744, 16940, 17056, 17149, 17221, 17268, 17424, 17496, 17664, 17833, 17840, 17864, 17885, 17889, 17905, 17916, 17940, 18069, 18085, 18108, 18117, 18132, 18177, 18337, 18396, 18409, 18496, 18513, 18732, 18765, 18805, 18841, 18865, 18872, 18920, 18985, 19165, 19212, 19232, 19272, 19280, 19292, 19360, 19376, 19428, 19592, 19644, 19725, 19761.

Some larger examples :