Problems & Puzzles: Puzzles

Puzzle 730. Trio of Consecutive Achilles numbers

An Achilles number is a number which is powerful but not a perfect power, like 72 = 23 * 32

According to G. Resta page, there are infinite pairs of consecutive Achilles numbers, the smallest being 5425069447 = 73 * 412 * 972, 5425069448 = 23 * 260412.

Q. Can you find the smallest trio of consecutive Achilles numbers or prove that they do not exist?


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