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centered triangular n.  and  powerful n.

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(max 15 digits)

First numbers that belong to both sets:

1, 4, 64, 361, 6241, 35344, 611524, 3463321, 59923081, 78528691, 339370084, 5871850384, 33254804881, 575381414521, 3258631508224, 56381506772644, 319312633001041.