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d-powerful n.  and  self n.

First numbers that belong to both sets:

1, 3, 5, 7, 9, 132, 209, 334, 378, 1234, 2134, 2224, 2246, 2314, 2336, 2628, 2773, 2863, 2953, 3212, 3214, 3236, 3706, 3943, 4114, 4136, 4158, 4248, 4316, 4573, 4685, 4933, 4955, 5328, 5653, 5833, 5877, 6935, 7363, 8206, 8263, 8443, 8623, 8667, 8825, 8970, 9723, 9725, 10693, 12695, 13393, 13933, 14697, 16363, 16431, 16453, 16475, 16543, 16857, 17241, 17443, 17847, 19243, 21236, 21258, 21348, 21785, 22338, 22393, 22573, 22595, 22663, 22753, 22955, 23036, 23473, 23563, 23697, 23743, 23945, 23967, 24316, 24373, 24597, 24621, 24643, 24687, 24733, 24755, 24823, 24845, 25273, 25431, 25453, 25677, 25723, 26241, 26443, 26533, 26555, 27253, 27343, 27365, 27433, 27635, 27747, 28265, 28355, 28423, 28737, 29435, 29637, 30236, 30348, 32743, 32787, 32833, 32877, 32899, 32923, 32945, 32989, 33026, 33228, 33261, 33283, 33318, 33823, 33957, 34038, 34295, 34677, 34947, 34980, 35083, 35285, 35487, 35937, 35992, 36253, 36275, 36343, 36567, 36657, 36723, 36837, 36892, 36982, 37221, 37243, 37265, 37421, 37423, 37827, 38345, 39423, 39425, 39469, 39627, 39682, 39827, 39884, 40685, 41697, 42048, 42261, 42608, 42687, 43363, 44645, 44735, 46713, 46737, 46770, 46792, 46825, 46939, 46972, 46994, 47016, 47367, 47692, 47962, 48245, 48289, 48625, 49323, 49727, 49729, 49762, 49784, 49896, 52723, 52745, 52789, 52857, 53263, 53487, 55827, 56749, 59067, 59223, 59247, 59269, 59392, 59752, 59796, 59930, 59932, 60351, 62353, 62397, 62599, 62645, 62667, 62735, 62825, 63297, 63321, 63343, 63387, 63433, 63477, 63679, 63723, 63725, 63769, 64197, 64333, 64445, 64737, 64792, 65523, 65839, 65894, 66245, 66357, 66423, 66425, 66480, 66884, 66974, 67323, 67325, 67413, 67549, 67639, 67672, 67727, 67729, 67896, 67929, 67942, 68225, 68425, 68449, 68640, 68976, 69237, 69349, 69472, 69729, 69742, 72343, 72747, 73423, 74233, 74323, 74345, 74659, 75974, 75996, 76323, 76325, 76369, 76929, 77223, 78349, 78527, 78540.

Some larger examples :