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d-powerful n.  and  powerful n.

First numbers that belong to both sets:

1, 4, 8, 9, 1323, 2048, 4225, 4624, 5324, 5329, 5832, 8712, 17424, 19773, 24336, 26244, 27436, 35912, 35937, 49729, 66049, 66248, 68644, 83349, 223729, 232324, 243675, 256036, 256328, 263169, 264627, 265837, 275427, 282752, 285768, 286225, 286443, 287296, 287496, 329623, 344569, 344763, 345600, 363312, 373321, 382347, 463347, 521752, 532512, 536648, 562432, 662596, 685584, 822649, 829472, 834632, 1347921, 1647243, 1758276, 1943236, 2053489, 2138312, 2179872, 2223963, 2226064, 2230272, 2232036, 2235025, 2238728, 2249728, 2298256, 2298368, 2325625, 2328676, 2356225, 2358792, 2362369, 2365444, 2367488, 2368521, 2383936, 2384928, 2392533, 2413827, 2426976, 2427364, 2436721, 2439844, 2534464, 2536828, 2544723, 2544768, 2579236, 2608225, 2634129, 2636984, 2637376, 2647129, 2663432, 2666689, 2676496, 2745649, 2756552, 2772225, 2775368, 2778889, 2866249, 2951524, 2968729, 3232332, 3232804, 3265249, 3267864, 3297856, 3322336, 3352561, 3441025, 3553225, 3568572, 3577392, 3580488, 3655744, 3666632, 3667225, 3742848, 3763584, 3786752, 3829849, 3857296, 3875328, 3904576, 3944312, 3962336, 4072324, 4210704, 4212675, 4253392, 4255443, 4264225, 4268356, 4286592, 4333568, 4341627, 4345352, 4347225, 4359744, 4371125, 4376464, 4392287, 4393216, 4428288, 4457628, 4472523, 4473225, 4476032, 4528384, 4562496, 4620375, 4657463, 4678569, 4734976, 4743684, 4853952, 4854728, 4857223, 4875264, 4954952, 5225796, 5239521, 5253125, 5322249, 5326864, 5359225, 5471432, 5597956, 5632792, 5787963, 5793649, 5832225, 5846724, 5909761, 5938947, 5938969, 5976432, 6322568, 6325225, 6328125, 6340324, 6344128, 6426225, 6436343, 6562323, 6635776, 6642376, 6682225, 6723027, 6723649, 6843744, 6874632, 6889472, 6927424, 6943225, 6953769, 7268416, 7472736, 7873636, 7924225, 8323225, 8454272, 8786432, 8892324, 8947775, 9255384, 9265936, 9273368, 9279432, 9972964.