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binomial coefficient  and  powerful n.

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(max 15 digits)

First numbers that belong to both sets:

36, 1225, 19600, 29403, 41616, 1413721, 48024900, 74024028, 1631432881, 27665282700, 55420693056, 1024060098375, 1665678432600, 1882672131025.