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PUZZLET 218

Achilles Numbers

A Powerful Number is one which has at least two of each of its Prime Factors, such as 200, with PFs 2, 2, 2, 5, 5. (three twos and two fives). Counter-example: 18 is NOT a Powerful Number. Its PFs are 2, 3, 3 (Only one 2).

An Achilles Number is a Powerful Number which additionally is neither a power of some other integer, nor prime, such as 72.

Find at least one Achilles Number whose digits form a "run", such as 67, 234, 6789, etc.




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Last Updated: June 20th, 2010.