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amenable n.  and  Ulam n.

First numbers that belong to both sets:

1, 8, 13, 16, 28, 36, 48, 53, 57, 69, 72, 77, 97, 145, 148, 177, 180, 189, 197, 209, 221, 236, 241, 253, 260, 273, 309, 316, 324, 341, 356, 400, 409, 412, 429, 441, 456, 485, 497, 524, 544, 568, 585, 605, 612, 624, 668, 673, 685, 688, 720, 732, 781, 800, 820, 849, 861, 864, 893, 905, 949, 1020, 1025, 1032, 1037, 1052, 1081, 1101, 1125, 1157, 1164, 1169, 1208, 1252, 1257, 1296, 1308, 1313, 1340, 1360, 1377, 1389, 1404, 1428, 1433, 1465, 1472, 1489, 1492, 1509, 1516, 1536, 1553, 1604, 1616, 1641, 1648, 1660, 1709, 1721, 1724, 1748, 1765, 1792, 1812, 1836, 1853, 1856, 1900, 1941, 1944, 1968, 1985, 2012, 2032, 2056, 2093, 2112, 2117, 2156, 2249, 2252, 2288, 2332, 2393, 2420, 2445, 2464, 2481, 2484, 2513, 2525, 2552, 2572, 2581, 2584, 2589, 2613, 2616, 2628, 2633, 2660, 2696, 2721, 2748, 2789, 2809, 2816, 2833, 2897, 2916, 2921, 2985, 3029, 3041, 3065, 3068, 3085, 3092, 3109, 3153, 3205, 3217, 3236, 3261, 3288, 3305, 3368, 3373, 3393, 3417, 3456, 3473, 3476, 3481, 3525, 3544, 3549, 3593, 3605, 3608, 3625, 3632, 3649, 3669, 3696, 3725, 3740, 3764, 3808, 3825, 3872, 3916, 3952, 3960, 4040, 4057, 4101, 4121, 4148, 4153, 4165, 4233, 4260, 4297, 4324, 4341, 4365, 4368, 4392, 4404, 4409, 4453, 4517, 4536, 4580, 4600, 4624, 4641, 4644, 4668, 4729, 4732, 4756, 4800, 4881, 4900, 4905, 4925, 4969, 4996, 5020, 5032, 5037, 5049, 5052, 5057, 5081, 5096, 5164, 5181, 5184, 5208, 5252, 5269, 5272, 5296, 5316, 5357, 5384, 5484, 5489, 5516, 5533, 5597, 5616, 5665, 5685, 5765, 5768, 5797, 5812, 5829, 5853, 5856, 5873, 5880, 5900, 5944, 6024, 6029, 6049, 6068, 6112, 6156, 6176, 6244, 6308, 6325, 6352.

Some larger examples :