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d-powerful n.  and  odious n.

First numbers that belong to both sets:

1, 2, 4, 7, 8, 224, 262, 283, 333, 334, 357, 370, 372, 375, 376, 379, 445, 463, 518, 598, 794, 849, 935, 1034, 1234, 1255, 1306, 1349, 1364, 1498, 1634, 1676, 1765, 2048, 2063, 2114, 2131, 2133, 2134, 2137, 2138, 2223, 2225, 2240, 2243, 2245, 2246, 2249, 2263, 2264, 2283, 2315, 2332, 2335, 2336, 2353, 2356, 2373, 2395, 2407, 2449, 2465, 2483, 2517, 2537, 2574, 2597, 2607, 2627, 2664, 2733, 2739, 2753, 2773, 2793, 2794, 2843, 2849, 2864, 2932, 2939, 2994, 3145, 3165, 3212, 3215, 3234, 3236, 3254, 3257, 3292, 3295, 3345, 3362, 3385, 3436, 3453, 3454, 3457, 3475, 3477, 3523, 3525, 3543, 3566, 3635, 3652, 3674, 3692, 3723, 3725, 3726, 3749, 3764, 3786, 3856, 3940, 3943, 3944, 3947, 3949, 4114, 4132, 4136, 4150, 4153, 4154, 4156, 4159, 4173, 4209, 4225, 4228, 4240, 4243, 4245, 4246, 4249, 4261, 4262, 4265, 4266, 4268, 4285, 4288, 4339, 4353, 4373, 4396, 4443, 4449, 4469, 4485, 4572, 4599, 4622, 4624, 4649, 4732, 4735, 4736, 4826, 4849, 4869, 4932, 4950, 4953, 4954, 4956, 4959, 5182, 5232, 5258, 5320, 5323, 5325, 5326, 5328, 5343, 5344, 5364, 5367, 5453, 5632, 5746, 5833, 5858, 5877, 5902, 6244, 6247, 6423, 6424, 6443, 6649, 6714, 6792, 6934, 6937, 6974, 6976, 7123, 7234, 7279, 7343, 7363, 7432, 7582, 7632, 7928, 8201, 8202, 8204, 8207, 8209, 8225, 8228, 8243, 8245, 8263, 8288, 8352, 8376, 8396, 8462, 8536, 8647, 8712, 8756, 8792, 8825, 8970, 8972, 8975, 8977, 8978, 9237, 9272, 9347, 9362, 9478, 9693, 9697, 9947, 9963, 10322, 10693, 10694, 10722, 12343, 12347, 12367, 12415, 12434, 12542, 12562, 12615, 12634, 12854, 13132, 13173, 13332, 13933, 14295, 14346, 14363, 14369, 14726, 14786, 15422, 15882, 16274, 16346, 16430, 16432, 16435, 16437, 16438, 16470, 16473.

Some larger examples :