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admirable n.  and  d-powerful n.

First numbers that belong to both sets:

24, 224, 1074, 1542, 2334, 2994, 3342, 3678, 3786, 4228, 4396, 5322, 6244, 7962, 8202, 8204, 9474, 9654, 10722, 15882, 16436, 16494, 17332, 17994, 20356, 23492, 24594, 27366, 27498, 28532, 28554, 28734, 29454, 32788, 32874, 32898, 33042, 33068, 33486, 33846, 33882, 33954, 34674, 34698, 34746, 36258, 36438, 36474, 36988, 37482, 37578, 37626, 37794, 38382, 39426, 39462, 39642, 39844, 41298, 43782, 43926, 46732, 46734, 46938, 46974, 47694, 49254, 49386, 49722, 53228, 53396, 56382, 56634, 56982, 57606, 59226, 59406, 59442, 59802, 62394, 63476, 63762, 63942, 64734, 64794, 65324, 65634, 65694, 65838, 65922, 66354, 66954, 67434, 73446, 74346, 74452, 74896, 75846, 78654, 79996, 82374, 82554, 84954, 85326, 85926, 87836, 91842, 93268, 93846, 93882, 94854, 95286, 96522, 98922, 99402, 123378, 124638, 126364, 126726, 127266, 132244, 132738, 132954, 133252, 133924, 134372, 137526, 138246, 138426, 138486, 138954, 139254, 142962, 145086, 145374, 145686, 146634, 147426, 151564, 156594, 157232, 158394, 164276, 166434, 166674, 167682, 169374, 172626, 177436, 182346, 184362, 192332, 192462, 193278, 193926, 194226, 194262, 196242, 196756, 198426, 198642, 203924, 205962, 206332, 209478, 213558, 222954, 223638, 223926, 224178, 224538, 224646, 224958, 225366, 225546, 229566, 232036, 232746, 232926, 233754, 233884, 234834, 234836, 234892, 236238, 236298, 236454, 236634, 237738, 238566, 241386, 242732, 242956, 242958, 243292, 243582, 243654, 243762, 243964, 244626, 245562, 247436, 249234, 249474, 249582, 249654, 249762, 249906, 252364, 253372, 253794, 255534, 256926, 257394, 259422, 259756, 262518, 262554, 262662, 262734, 262758, 263346, 263478, 263564, 263658, 263838, 263922, 263946, 264246, 264318, 264354, 264426, 264534, 264666, 264714, 264738, 264774, 265218, 265412, 265494, 265542, 265748, 266334, 267258, 267474, 267522, 268734, 269034, 269274, 269322, 269454, 269634, 269922, 271398, 272524, 272562, 272634, 272946, 272982, 273594, 273868, 273954, 274036, 274542, 274674, 274962, 276272, 277374, 278634, 279042, 279248, 279354, 282354, 282558, 282666, 282738, 283216, 283326, 283674, 283722.

Some larger examples :