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d-powerful n.  and  emirpimes

First numbers that belong to both sets:

226, 629, 794, 1234, 1306, 1765, 2062, 2245, 2263, 2443, 2449, 2627, 3215, 3385, 3437, 3453, 3543, 3635, 3946, 3949, 4151, 4573, 4574, 4735, 4954, 4955, 5182, 5327, 5329, 5342, 5366, 5567, 5833, 5873, 6443, 6649, 7279, 7343, 9122, 9347, 9493, 10694, 12367, 12434, 12634, 13133, 13173, 13373, 13393, 14786, 16213, 16438, 16439, 16474, 16743, 17133, 17243, 17245, 17249, 17287, 17338, 17378, 17463, 17849, 18697, 18946, 19243, 20203, 20843, 22249, 22333, 22373, 22463, 22465, 22489, 22537, 22595, 22597, 22663, 22735, 22823, 22955, 22978, 24226, 24289, 24397, 24643, 24667, 24737, 24754, 24757, 24823, 24883, 24994, 26443, 26483, 28553, 32743, 32815, 32834, 32873, 32891, 32986, 33221, 33262, 33265, 33266, 33398, 33622, 33685, 33778, 33779, 33842, 34234, 34291, 34387, 34766, 34834, 34982, 34987, 35087, 35285, 35885, 35935, 35939, 35978, 36122, 36253, 36327, 36382, 36437, 36983, 36987, 37227, 37229, 37267, 37358, 37462, 38257, 38474, 38527, 38834, 39533, 39682, 43478, 43523, 43762, 47695, 47962, 49562, 49721, 53282, 53483, 53489, 53843, 54566, 55402, 55466, 55483, 59249, 59269, 59282, 59578, 59935, 60355, 60359, 60595, 60938, 62179, 62357, 62395, 62519, 62663, 62669, 62735, 62797, 64247, 64289, 64463, 64555, 64573, 64687, 64795, 66353, 66358, 66487, 66623, 66938, 66995, 68245, 71662, 73426, 73642, 73649, 74234, 74659, 75643, 75934, 76237, 76453, 76894, 76927, 78145, 78349, 78454, 78503, 78527, 78655, 78922, 78963, 79045, 79595, 79683, 79759, 81253, 83254, 85433, 85477, 89497, 91829, 92273, 92303, 92343, 92362, 92522, 92542, 92654, 92677, 93421, 93667, 94474, 95246, 95797, 96542, 96567, 97466, 97733, 98437, 98493, 99602, 104893, 105394, 106439, 106499, 112226, 112262, 117903, 117983, 118397, 119857, 121537, 122479, 122783, 123223, 123283, 123537, 124237, 124307, 124499, 124639, 124694, 124833, 124923, 124966, 125283, 125447, 125486, 125733, 125957, 126146, 126163, 126299, 126329, 126347, 126389, 126479, 126523, 126674, 126767, 127486.

Some larger examples :