Over at his blog, Ken is investigating top-heavy perfect powers to investigate increasing the breadth of the Cunningham project. He makes a list of 2413 perfect powers bn with bn in increasing order, up to a googol, omitting bases that are themselves perfect powers (for instance, 4n, 8n or 9n).

Your task is to make a list of the 2413 top-heavy perfect powers less than a googol. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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