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evil n.  and  untouchable n.

First numbers that belong to both sets:

5, 96, 120, 210, 216, 238, 246, 288, 306, 326, 408, 430, 474, 498, 516, 520, 540, 556, 562, 576, 612, 624, 658, 670, 708, 718, 726, 732, 748, 756, 766, 768, 792, 802, 804, 836, 848, 894, 898, 934, 966, 996, 1028, 1046, 1068, 1074, 1080, 1128, 1134, 1146, 1148, 1162, 1186, 1192, 1200, 1212, 1248, 1254, 1258, 1266, 1272, 1314, 1316, 1326, 1346, 1348, 1360, 1388, 1406, 1422, 1506, 1508, 1542, 1566, 1596, 1632, 1642, 1650, 1680, 1692, 1716, 1728, 1746, 1758, 1774, 1776, 1806, 1820, 1830, 1842, 1844, 1866, 1896, 1920, 1944, 1956, 1960, 1986, 1992, 2010, 2022, 2036, 2050, 2052, 2062, 2098, 2118, 2136, 2148, 2152, 2158, 2196, 2212, 2248, 2262, 2302, 2304, 2316, 2322, 2324, 2338, 2364, 2376, 2410, 2430, 2436, 2446, 2454, 2464, 2482, 2484, 2496, 2502, 2514, 2530, 2572, 2590, 2600, 2606, 2608, 2614, 2628, 2640, 2704, 2726, 2758, 2762, 2788, 2824, 2914, 2944, 2950, 2968, 2978, 2984, 2992, 3036, 3060, 3072, 3078, 3102, 3126, 3132, 3144, 3152, 3162, 3174, 3186, 3198, 3202, 3208, 3228, 3238, 3270, 3276, 3312, 3318, 3356, 3366, 3378, 3384, 3402, 3412, 3422, 3428, 3432, 3476, 3486, 3504, 3510, 3524, 3564, 3576, 3588, 3592, 3600, 3636, 3648, 3666, 3682, 3684, 3708, 3746, 3748, 3752, 3758, 3760, 3792, 3808, 3818, 3820, 3828, 3832, 3860, 3876, 3888, 3900, 3936, 3942, 3954, 3960, 3972, 3982, 4018, 4032, 4056, 4062, 4068, 4072, 4078, 4086, 4098, 4104, 4148, 4170, 4172, 4184, 4190, 4206, 4224, 4248, 4258, 4296, 4302, 4304, 4316, 4320, 4344, 4370, 4382, 4386, 4388, 4406, 4430, 4472, 4488, 4506, 4512, 4530, 4574, 4580, 4614, 4618, 4648, 4662, 4668, 4686, 4688, 4700, 4710, 4738, 4740, 4750, 4758, 4764, 4830, 4840, 4854, 4860, 4868.

Some larger examples :