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d-powerful n.  and  palprime

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(max 15 digits)

First numbers that belong to both sets:

2, 3, 5, 7, 373, 98389, 3223223, 3245423, 3307033, 3425243, 3427243, 3479743, 3673763, 3765673, 7327237, 7365637, 7521257, 9255529, 9271729, 9749479.