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d-powerful n.  and  sphenic n.

First numbers that belong to both sets:

357, 370, 374, 518, 598, 935, 994, 1034, 1074, 1498, 1542, 1634, 2114, 2134, 2135, 2139, 2242, 2247, 2314, 2334, 2355, 2373, 2379, 2445, 2465, 2607, 2626, 2737, 2739, 2794, 2849, 2994, 3145, 3165, 3237, 3298, 3342, 3345, 3435, 3454, 3477, 3657, 3674, 3678, 3706, 3723, 3765, 3786, 3945, 4154, 4155, 4173, 4209, 4245, 4246, 4355, 4403, 4623, 4738, 4826, 4953, 4958, 5258, 5322, 5343, 5453, 5858, 5902, 6603, 6794, 6935, 6974, 7329, 7582, 7906, 7962, 8202, 8205, 8206, 8245, 8283, 8974, 8979, 9273, 9362, 9474, 9478, 9654, 9723, 10322, 10722, 12345, 12415, 12562, 13978, 14295, 14362, 14722, 14726, 15422, 15423, 15882, 16274, 16346, 16435, 16471, 16494, 16742, 16942, 17241, 17242, 17445, 17841, 17842, 17845, 17994, 20377, 20539, 21235, 21345, 21497, 21835, 22195, 22243, 22263, 22269, 22334, 22335, 22355, 22358, 22378, 22395, 22538, 22539, 22557, 22593, 22953, 22954, 22958, 23162, 23235, 23253, 23295, 23326, 23343, 23387, 23433, 23435, 23439, 23493, 23498, 23522, 23582, 23583, 23617, 23673, 23727, 23745, 23749, 23858, 23907, 23943, 23947, 24245, 24265, 24423, 24590, 24591, 24594, 24621, 24622, 24626, 24681, 24739, 24753, 25214, 25322, 25323, 25327, 25366, 25430, 25437, 25473, 25653, 26243, 26245, 26246, 26247, 26426, 26427, 26537, 26555, 26593, 27237, 27322, 27326, 27345, 27347, 27363, 27365, 27366, 27498, 28262, 28355, 28554, 28731, 28734, 28735, 29454, 29967, 30349, 31558, 32326, 32342, 32635, 32782, 32785, 32813, 32818, 32857, 32874, 32893, 32898, 32907, 32923, 32926, 32943, 32945, 32963, 32965, 32981, 33027, 33042, 33087, 33226, 33229, 33242, 33263, 33267, 33269, 33338, 33422, 33429, 33442, 33486, 33538, 33578, 33826, 33843, 33846, 33847, 33865, 33882, 33954, 34235, 34237, 34239, 34279, 34294, 34298, 34323, 34474, 34498, 34526, 34529, 34562, 34674, 34698, 34746, 34922, 34989, 35085, 35086, 35203, 35205, 35222, 35223, 35247, 35662, 35738.

Some larger examples :