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d-powerful n.  and  evil n.

First numbers that belong to both sets:

3, 5, 6, 9, 24, 43, 63, 89, 132, 135, 153, 175, 209, 226, 264, 267, 332, 371, 373, 374, 377, 378, 407, 629, 739, 994, 1073, 1074, 1323, 1326, 1386, 1542, 1672, 1836, 2062, 2064, 2083, 2130, 2132, 2135, 2136, 2139, 2179, 2194, 2203, 2205, 2224, 2227, 2241, 2242, 2244, 2247, 2248, 2314, 2333, 2334, 2352, 2355, 2372, 2376, 2379, 2394, 2396, 2423, 2427, 2443, 2445, 2464, 2532, 2536, 2554, 2572, 2577, 2623, 2626, 2628, 2645, 2735, 2737, 2738, 2757, 2792, 2803, 2824, 2863, 2933, 2934, 2953, 2973, 3147, 3167, 3214, 3235, 3237, 3238, 3252, 3255, 3274, 3294, 3298, 3324, 3342, 3432, 3435, 3437, 3474, 3476, 3492, 3496, 3527, 3569, 3612, 3657, 3678, 3706, 3746, 3765, 3941, 3942, 3945, 3946, 3948, 4133, 4151, 4152, 4155, 4157, 4158, 4194, 4224, 4241, 4242, 4244, 4247, 4248, 4260, 4263, 4264, 4267, 4269, 4316, 4332, 4352, 4355, 4397, 4403, 4405, 4424, 4447, 4573, 4574, 4623, 4644, 4648, 4685, 4733, 4738, 4933, 4951, 4952, 4955, 4957, 4958, 5236, 5259, 5276, 5321, 5322, 5324, 5327, 5329, 5342, 5366, 5384, 5432, 5547, 5562, 5567, 5653, 5657, 5766, 5832, 5873, 6249, 6579, 6603, 6669, 6732, 6793, 6794, 6849, 6932, 6935, 6939, 6972, 7032, 7296, 7299, 7323, 7329, 7639, 7836, 7906, 7944, 7962, 7964, 8200, 8203, 8205, 8206, 8208, 8223, 8224, 8262, 8283, 8289, 8316, 8443, 8623, 8667, 8864, 8932, 8971, 8973, 8974, 8976, 8979, 9122, 9234, 9236, 9273, 9274, 9324, 9342, 9385, 9474, 9493, 9654, 9723, 9725, 10723, 12298, 12324, 12345, 12432, 12495, 12695, 12723, 13133, 13337, 13373, 13393, 13443, 13532, 13978, 14276, 14362, 14697, 14722, 15423, 15686, 15822, 16213, 16234, 16293, 16363, 16431, 16433, 16434, 16436, 16439, 16453, 16471, 16472, 16475, 16477, 16478, 16494, 16524, 16729.

Some larger examples :