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d-powerful n.  and  frugal n.

First numbers that belong to both sets:

2048, 5329, 23763, 24334, 24353, 24576, 26244, 34295, 35287, 49729, 59375, 66049, 83349, 85293, 124659, 134977, 137543, 139258, 143750, 182493, 184493, 187353, 194643, 207279, 214273, 216763, 223293, 230496, 230839, 235264, 236927, 238383, 239375, 243968, 245673, 247303, 249307, 249344, 256907, 257337, 262205, 262440, 263169, 264627, 267543, 269941, 272473, 274432, 276875, 278125, 282752, 284375, 285610, 287296, 289413, 294637, 295245, 303993, 306909, 314375, 322947, 325863, 326875, 329623, 336069, 337747, 339968, 340942, 344569, 345625, 345845, 347648, 352843, 354375, 354482, 358649, 365229, 365403, 375296, 382725, 464375, 533125, 534357, 542659, 546875, 562432, 571438, 623295, 639333, 642249, 657443, 690363, 723243, 734375, 766322, 794624, 822649, 898857, 924385, 1045937, 1048727, 1078375, 1148375, 1227755, 1232375, 1232579, 1234197, 1238593, 1243667, 1245824, 1252422, 1253632, 1274593, 1326592, 1336257, 1344223, 1346463, 1347921, 1355317, 1358127, 1365784, 1372343, 1372672, 1375137, 1403392, 1424293, 1436827, 1446767, 1523853, 1541875, 1557827, 1562247, 1599375, 1602233, 1602839, 1603643, 1613472, 1628343, 1642437, 1642923, 1643776, 1645353, 1652423, 1662363, 1665737, 1666294, 1680345, 1684349, 1691523, 1699328, 1714637, 1720683, 1726319, 1726976, 1732347, 1736875, 1739264, 1742336, 1746441, 1762334, 1763767, 1764375, 1764735, 1778432, 1782359, 1823229, 1837217, 1843625, 1873125, 1879297, 1926974, 1957376, 1959424, 1959803, 1964375, 1966336, 1974527, 2022935, 2022975, 2032255, 2035625, 2035712, 2046953, 2048247, 2053289, 2053489, 2053593, 2065743, 2073065, 2079266, 2084953, 2085632, 2097333, 2098853, 2121390, 2121843, 2122496, 2123577, 2126413, 2126493, 2130625, 2132224, 2133297, 2133783, 2134269, 2134489, 2138886, 2144239, 2145933, 2146875, 2147466, 2148363, 2148895, 2158739, 2162943, 2179072, 2195456, 2204375, 2206683, 2212693, 2213643, 2215424, 2215936, 2216875, 2219264, 2222336, 2223693, 2224179, 2224375, 2226064, 2226688, 2228224, 2228553, 2229039, 2230528, 2230529, 2230784, 2231469, 2232832, 2232851, 2232927, 2233155, 2234325, 2234385, 2235114, 2235136, 2235331, 2235357, 2235625, 2235843, 2236329, 2236672, 2238728, 2239375, 2241675, 2242534, 2245563, 2246049, 2246535, 2246993, 2247679, 2248448, 2248751, 2249728, 2253287, 2254963, 2255283, 2256255, 2257664, 2258368, 2259375, 2259938, 2262573, 2263457, 2263545, 2264375, 2264576, 2264645, 2265344, 2267569.

Some larger examples :