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Lynch-Bell n.  and  powerful n.

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First numbers that belong to both sets:

1, 4, 8, 9, 36, 128, 216, 324, 432, 648, 784, 864, 1296, 1764, 2916, 6912, 9216, 13824, 18432, 84672, 314928, 1382976, 9176328.