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amenable n.  and  untouchable n.

First numbers that belong to both sets:

5, 52, 88, 96, 120, 124, 188, 216, 248, 268, 276, 288, 292, 304, 324, 336, 372, 408, 448, 472, 516, 520, 540, 552, 556, 576, 584, 612, 624, 628, 668, 708, 732, 748, 756, 768, 784, 792, 804, 836, 848, 852, 872, 892, 896, 936, 964, 976, 996, 1028, 1044, 1060, 1068, 1080, 1116, 1128, 1148, 1160, 1168, 1180, 1192, 1200, 1212, 1236, 1248, 1256, 1272, 1288, 1296, 1312, 1316, 1332, 1348, 1360, 1380, 1388, 1404, 1420, 1476, 1508, 1528, 1588, 1596, 1632, 1680, 1692, 1716, 1728, 1732, 1776, 1816, 1820, 1840, 1844, 1852, 1860, 1884, 1888, 1896, 1920, 1944, 1956, 1960, 1972, 1992, 2008, 2024, 2036, 2048, 2052, 2068, 2096, 2108, 2120, 2128, 2136, 2148, 2152, 2168, 2196, 2212, 2228, 2232, 2248, 2304, 2316, 2324, 2356, 2364, 2376, 2388, 2404, 2408, 2416, 2432, 2436, 2452, 2464, 2484, 2496, 2500, 2564, 2568, 2572, 2576, 2588, 2600, 2608, 2628, 2640, 2704, 2724, 2736, 2748, 2760, 2784, 2788, 2808, 2824, 2828, 2856, 2876, 2932, 2944, 2952, 2968, 2984, 2992, 2996, 3008, 3028, 3036, 3060, 3072, 3076, 3104, 3132, 3136, 3144, 3152, 3156, 3208, 3228, 3236, 3276, 3292, 3296, 3312, 3328, 3340, 3356, 3384, 3388, 3396, 3400, 3412, 3420, 3428, 3432, 3448, 3476, 3484, 3488, 3504, 3524, 3556, 3564, 3576, 3580, 3588, 3592, 3600, 3604, 3636, 3648, 3652, 3656, 3684, 3708, 3744, 3748, 3752, 3760, 3788, 3792, 3808, 3812, 3816, 3820, 3828, 3832, 3860, 3868, 3872, 3876, 3888, 3900, 3904, 3936, 3940, 3960, 3972, 4032, 4036, 4048, 4056, 4068, 4072, 4088, 4104, 4116, 4120, 4148, 4168, 4172, 4184, 4188, 4216, 4224, 4248, 4268, 4280, 4296, 4304, 4308, 4312, 4316, 4320, 4336, 4344, 4356, 4368, 4380, 4388, 4396, 4416, 4472, 4476, 4480, 4488.

Some larger examples :