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d-powerful n.  and  Zumkeller n.

First numbers that belong to both sets:

6, 24, 132, 224, 264, 372, 378, 1074, 1326, 1386, 1542, 1672, 1836, 2064, 2130, 2136, 2205, 2240, 2244, 2334, 2352, 2376, 2394, 2464, 2532, 2574, 2628, 2664, 2994, 3234, 3252, 3294, 3324, 3342, 3432, 3496, 3612, 3678, 3726, 3786, 3940, 3942, 3944, 3948, 4136, 4152, 4158, 4224, 4228, 4240, 4242, 4248, 4260, 4264, 4266, 4288, 4332, 4352, 4396, 4424, 4644, 4648, 4732, 4736, 4950, 4956, 5232, 5236, 5320, 5322, 5328, 5432, 5562, 5632, 5766, 6244, 6424, 6732, 6792, 6972, 6976, 7032, 7296, 7632, 7836, 7944, 7962, 8200, 8202, 8204, 8208, 8228, 8262, 8288, 8316, 8352, 8376, 8536, 8792, 8932, 8970, 8976, 9234, 9272, 9324, 9342, 9474, 9654, 10722, 12324, 12432, 13132, 13332, 15822, 15882, 16432, 16434, 16436, 16470, 16476, 16494, 16524, 16984, 17240, 17248, 17332, 17334, 17376, 17448, 17840, 17844, 17868, 17994, 18522, 18872, 20064, 20332, 20352, 20356, 20532, 21364, 22332, 22338, 22372, 22374, 22624, 22848, 22932, 22950, 22956, 22995, 23034, 23056, 23232, 23274, 23324, 23364, 23436, 23452, 23472, 23492, 23496, 23548, 23562, 23568, 23584, 23634, 23652, 23744, 23748, 23856, 23892, 23928, 23988, 24332, 24376, 24396, 24426, 24464, 24576, 24592, 24594, 24596, 24620, 24624, 24680, 24684, 24750, 24752, 24756, 24792, 24840, 24846, 24864, 24936, 24976, 24996, 25232, 25254, 25272, 25432, 25434, 25476, 25494, 25764, 25872, 26224, 26240, 26352, 26394, 26448, 26574, 26736, 27234, 27324, 27360, 27366, 27368, 27472, 27498, 27984, 28260, 28266, 28336, 28532, 28536, 28554, 28730, 28734, 28932, 29232, 29346, 29436, 29454, 29634, 29744, 29835, 30340, 30342, 30348, 32052, 32256, 32364, 32436, 32528, 32562, 32780, 32784, 32788, 32816, 32830, 32832, 32838, 32872, 32874, 32890, 32892, 32898, 32922, 32940, 32944, 32946, 32968, 32980, 32982, 32984, 32988, 33020, 33024, 33042, 33068, 33220, 33222, 33228, 33260, 33264, 33288, 33318, 33372, 33486.

Some larger examples :