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d-powerful n.  and  lucky n.

First numbers that belong to both sets:

1, 3, 7, 9, 43, 63, 135, 267, 283, 357, 463, 739, 1323, 1765, 2083, 2133, 2283, 2335, 2355, 2379, 2395, 2407, 2427, 2445, 2607, 2773, 2953, 2973, 3235, 3453, 3477, 3943, 4173, 4263, 4269, 4285, 4443, 4485, 4573, 4623, 4951, 5259, 5325, 5343, 5547, 5833, 6249, 6669, 6849, 6937, 7279, 7299, 7639, 8223, 8263, 8283, 8289, 8647, 8977, 8979, 9273, 10723, 12495, 13443, 16213, 16431, 16473, 16479, 17157, 17287, 17463, 17737, 19773, 20203, 20355, 20539, 20887, 21345, 22269, 22333, 22533, 22597, 22953, 22957, 23295, 23343, 23365, 23523, 23529, 23563, 23835, 23857, 23925, 23943, 24289, 24397, 24423, 24591, 24643, 24669, 24733, 24739, 24759, 24843, 24865, 25237, 25389, 25431, 25477, 25657, 25677, 26313, 26533, 26845, 27237, 27349, 27363, 27417, 27493, 27639, 27765, 28245, 28375, 28513, 28593, 28735, 29253, 29349, 32325, 32635, 32637, 32833, 32923, 32985, 33021, 33027, 33247, 33757, 33843, 34233, 34293, 34323, 34387, 34873, 35203, 35205, 35221, 35223, 35287, 35427, 35625, 36277, 36417, 36547, 36837, 36877, 36987, 37263, 37267, 37393, 37663, 38145, 38325, 38527, 38563, 39627, 39825, 41697, 41727, 42243, 42759, 43983, 44641, 44649, 46683, 46713, 46717, 46735, 46737, 46791, 46795, 46797, 46939, 47697, 49723, 50367, 52701, 52857, 54259, 54369, 54655, 54855, 56439, 56563, 56673, 59245, 59263, 59283, 59353, 59443, 59791, 59823, 59863, 59913, 60337, 60355, 60483, 60595, 62425, 62449, 62625, 62643, 62733, 62797, 63321, 63325, 63387, 63457, 63471, 63475, 63495, 63547, 63549, 63637, 63763, 63765, 64197, 64267, 64333, 64449, 64597, 65343, 65493, 65839, 66049, 66249, 66355, 66445, 66489, 66939, 67293, 67329, 67473, 67693, 67923, 67929, 67947, 67965, 68425, 68449, 68643, 69237, 69343, 69435, 69727, 69729, 69787, 72235, 73249, 73465, 73537, 74293, 74349, 74503, 75229, 75937, 75991, 75993, 76149, 76233, 76239, 77223, 77245, 78145, 78253, 78657, 79045, 79593, 79623, 79683.

Some larger examples :