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amenable n.  and  d-powerful n.

First numbers that belong to both sets:

1, 5, 8, 9, 24, 89, 132, 153, 209, 224, 264, 332, 333, 357, 372, 373, 376, 377, 445, 629, 849, 1073, 1349, 1364, 1672, 1676, 1765, 1836, 2048, 2064, 2132, 2133, 2136, 2137, 2205, 2224, 2225, 2240, 2241, 2244, 2245, 2248, 2249, 2264, 2332, 2333, 2336, 2352, 2353, 2356, 2372, 2373, 2376, 2396, 2445, 2449, 2464, 2465, 2517, 2532, 2536, 2537, 2572, 2577, 2597, 2628, 2645, 2664, 2733, 2737, 2753, 2757, 2773, 2792, 2793, 2824, 2849, 2864, 2932, 2933, 2953, 2973, 3145, 3165, 3212, 3236, 3237, 3252, 3257, 3292, 3324, 3345, 3385, 3432, 3436, 3437, 3453, 3457, 3476, 3477, 3492, 3496, 3525, 3569, 3612, 3652, 3657, 3692, 3725, 3749, 3764, 3765, 3856, 3940, 3941, 3944, 3945, 3948, 3949, 4132, 4133, 4136, 4152, 4153, 4156, 4157, 4173, 4209, 4224, 4225, 4228, 4240, 4241, 4244, 4245, 4248, 4249, 4260, 4261, 4264, 4265, 4268, 4269, 4285, 4288, 4316, 4332, 4352, 4353, 4373, 4396, 4397, 4405, 4424, 4449, 4469, 4485, 4572, 4573, 4624, 4644, 4648, 4649, 4685, 4732, 4733, 4736, 4849, 4869, 4932, 4933, 4952, 4953, 4956, 4957, 5232, 5236, 5276, 5320, 5321, 5324, 5325, 5328, 5329, 5344, 5364, 5384, 5432, 5453, 5632, 5653, 5657, 5832, 5833, 5873, 5877, 6244, 6249, 6424, 6649, 6669, 6732, 6792, 6793, 6849, 6932, 6937, 6972, 6976, 7032, 7296, 7329, 7432, 7632, 7836, 7928, 7944, 7964, 8200, 8201, 8204, 8205, 8208, 8209, 8224, 8225, 8228, 8245, 8288, 8289, 8316, 8352, 8376, 8396, 8536, 8712, 8756, 8792, 8825, 8864, 8932, 8972, 8973, 8976, 8977, 9236, 9237, 9272, 9273, 9324, 9385, 9493, 9693, 9697, 9725, 10693, 12324, 12345, 12432, 13132, 13133, 13173, 13332, 13337, 13373, 13393, 13532, 13933, 14276, 14369, 14697, 16213, 16293, 16432, 16433, 16436, 16437, 16453, 16472, 16473.

Some larger examples :