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d-powerful n.  and  happy n.

First numbers that belong to both sets:

1, 7, 226, 262, 376, 379, 739, 1323, 2062, 2063, 2133, 2224, 2242, 2245, 2333, 2396, 2517, 2554, 2572, 2574, 2933, 3238, 3436, 3635, 3692, 3706, 4157, 4225, 4248, 4285, 4447, 4449, 4572, 4599, 4959, 5182, 5364, 6932, 7363, 8200, 8225, 8245, 8396, 8973, 8975, 8976, 9236, 9362, 12347, 12562, 13332, 13393, 13933, 16363, 16471, 16524, 17240, 17243, 17244, 17287, 17357, 17424, 17443, 17483, 17840, 17843, 18347, 19736, 20572, 20752, 20933, 21348, 21564, 21743, 21835, 22249, 22267, 22269, 22372, 22374, 22375, 22378, 22467, 22537, 22573, 22595, 22732, 22735, 22738, 22753, 22954, 22955, 23272, 23274, 23275, 23417, 23454, 23472, 23474, 23527, 23744, 23745, 23812, 23963, 24137, 24229, 24372, 24375, 24423, 24483, 24576, 24592, 24598, 24627, 24683, 24735, 24750, 24753, 24756, 24823, 24840, 24843, 24863, 25237, 25272, 25273, 25294, 25327, 25434, 25435, 25437, 25453, 25473, 25476, 25526, 25562, 25657, 25723, 25764, 25942, 26247, 26339, 26393, 26427, 26483, 26574, 27052, 27129, 27234, 27253, 27322, 27324, 27345, 27617, 27697, 27747, 28132, 28261, 28265, 28423, 28513, 28732, 28738, 30346, 32275, 32527, 32782, 32788, 32811, 32812, 32814, 32815, 32830, 32839, 32872, 32893, 32899, 32903, 32963, 32983, 32989, 33021, 33023, 33028, 33029, 33266, 33269, 33338, 33539, 33829, 34036, 34217, 34254, 34272, 34274, 34472, 34525, 34542, 34987, 35227, 35245, 35247, 35427, 35845, 35933, 35938, 36239, 36343, 36637, 36789, 36837, 36980, 36986, 36987, 37222, 37224, 37225, 37228, 37242, 37244, 37421, 37422, 37424, 37425, 37442, 37663, 38124, 38272, 39533, 39538, 39608, 39623, 39687, 39823, 41218, 41382, 42048, 42242, 42243, 42267, 42483, 42534, 42598, 42683, 42863, 43363, 43525, 43527, 43542, 43544, 44283, 44372, 44644, 44645, 44647, 45237, 45583, 45835, 46711, 46799, 46823, 46935, 46953, 46959, 46979, 46994, 47256, 47652, 47699, 49784, 49897, 50724, 51862, 52294, 52344, 52498, 52526, 52701, 52702, 52704.

Some larger examples :