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d-powerful n.  and  Honaker prime

First numbers that belong to both sets:

2803, 4153, 4397, 12347, 13933, 24733, 24841, 26339, 35227, 54727, 86243, 133271, 136247, 137437, 146323, 182233, 205783, 213263, 223637, 230567, 243149, 243239, 243343, 249233, 249329, 271393, 272813, 274163, 284267, 285473, 285631, 299623, 308293, 309223, 321289, 325643, 326611, 328637, 334289, 341269, 341623, 343667, 344363, 344543, 346309, 346349, 346369, 348259, 348563, 348583, 349423, 356333, 360257, 362143, 423587, 432637, 432743, 435623, 443413, 479533, 505283, 522763, 525353, 526741, 528053, 531581, 538423, 595963, 598463, 623327, 623893, 633427, 633467, 644261, 652237, 672293, 672323, 672493, 673223, 692273, 722341, 723623, 823637, 824647, 835937, 872453, 877423, 978643, 1033783, 1049227, 1066343, 1088419, 1225997, 1226857, 1232227, 1233497, 1236229, 1244363, 1247243, 1275563, 1582463, 1623539, 1626437, 1642033, 1695233, 1726139, 1726661, 1942627, 2032561, 2048353, 2077351, 2107883, 2108543, 2122837, 2123263, 2123557, 2123867, 2123917, 2124631, 2126363, 2133059, 2135723, 2136773, 2136863, 2137259, 2138429, 2147359, 2156269, 2159473, 2159783, 2163443, 2213623, 2222263, 2223037, 2223563, 2223833, 2224553, 2225389, 2226227, 2226373, 2226793, 2227543, 2227943, 2228351, 2229527, 2234503, 2235227, 2235803, 2236417, 2236831, 2238233, 2242663, 2243383, 2243693, 2244863, 2246683, 2247257, 2247691, 2248373, 2252233, 2258233, 2258363, 2262629, 2262889, 2267413, 2273533, 2274523, 2275283, 2275393, 2276921, 2282173, 2285363, 2285653, 2287529, 2287921, 2290369, 2290493, 2303489, 2323423, 2327153, 2333657, 2333783, 2336263, 2340727, 2343223, 2343533, 2344187, 2345537, 2348743, 2349313, 2352353, 2355233, 2355253, 2357617, 2363047, 2364437, 2365423, 2365829, 2372119, 2372423, 2378423, 2379631, 2380853, 2385209, 2386217, 2395763, 2404733, 2405387, 2406263, 2406643, 2406683, 2413823, 2418943, 2425433, 2425453, 2425523, 2434387, 2434657, 2434727, 2437559, 2437973, 2439067, 2444357, 2447833, 2453177, 2462353, 2465143, 2465251, 2467307, 2482553, 2495203, 2502343, 2504329, 2506723, 2519273, 2523173, 2524343, 2524567, 2525531, 2525629, 2526239, 2530049, 2533367, 2533747, 2536447, 2539073, 2543423, 2544253, 2544383, 2548631, 2552393, 2553637, 2554283, 2554469, 2560343, 2562239, 2564329, 2566327, 2566433, 2567533, 2567933, 2568703, 2586277, 2594063, 2597723, 2598733, 2628809, 2629651, 2632523, 2632543, 2633207, 2635313, 2636233, 2642333, 2642771, 2643743, 2644139, 2644429, 2644849, 2645257.

Some larger examples :