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d-powerful n.  and  interprime n.

First numbers that belong to both sets:

4, 6, 9, 334, 370, 376, 994, 1234, 1364, 2130, 2134, 2139, 2205, 2241, 2247, 2336, 2379, 2396, 2554, 2627, 2794, 2933, 3165, 3252, 3255, 3345, 3453, 3723, 3764, 3786, 3945, 4136, 4155, 4158, 4224, 4242, 4248, 4260, 4266, 4332, 4353, 4403, 4449, 4685, 4932, 4954, 5232, 5276, 5328, 5366, 5384, 5746, 5833, 6424, 6579, 6603, 6714, 6792, 6849, 6932, 6974, 8200, 8289, 8970, 9342, 9693, 12345, 16430, 16479, 16524, 16857, 16984, 17248, 17845, 18347, 18436, 18522, 19243, 19733, 20355, 21258, 22358, 22375, 22536, 22558, 22593, 22733, 22773, 22952, 23034, 23076, 23239, 23274, 23292, 23295, 23324, 23348, 23439, 23562, 23587, 23745, 23764, 23943, 24226, 24372, 24376, 24627, 24680, 24687, 24756, 24796, 24844, 24849, 24868, 24883, 25257, 25346, 25431, 26243, 26313, 26352, 26379, 26427, 26443, 26807, 27256, 27349, 27364, 27498, 27639, 27765, 28554, 28955, 29343, 29385, 29637, 29835, 30344, 32235, 32325, 32562, 32781, 32786, 32817, 32832, 32836, 32898, 32940, 32949, 32963, 32985, 33026, 33087, 33267, 33288, 33442, 33512, 33828, 34036, 34256, 34290, 34299, 34323, 34528, 34698, 34874, 35082, 35086, 35224, 35358, 35372, 35845, 36296, 36342, 36348, 36454, 36567, 36789, 36988, 37220, 37248, 37263, 37486, 37626, 37732, 37884, 38324, 38456, 38522, 39372, 39429, 39627, 39844, 42248, 42269, 42759, 42973, 43434, 43542, 43782, 44644, 44649, 44735, 46713, 46737, 46770, 46809, 46824, 46975, 47306, 47690, 48667, 49238, 49368, 49542, 49785, 52362, 52523, 52542, 52703, 52724, 52763, 53088, 53356, 54369, 54873, 55626, 56364, 57378, 59066, 59202, 59227, 59241, 59373, 59442, 59596, 59736, 59794, 59883, 60595, 61654, 62139, 62409, 62463, 62594, 62646, 62976, 63290, 63324, 63342, 63364, 63470, 63568, 63706, 63723, 63767, 63987, 64445, 64572, 64624, 64732, 65693, 65704, 65724, 65783, 65838, 66044, 66353, 66393, 66623, 66937, 66954, 67184, 67323, 67346, 67896, 67929, 68574, 68649, 69146.

Some larger examples :