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Problem #402

Powerful Numbers I
 Public ★(x14) 06/23/17 by Philippe_57721 9xp Math 16.9%

A number is said powerful if all its prime factors appear with an exponent greater than 1.
A pure powerful number is a powerful number that is not a perfect square.

Two pure powerful numbers can be consecutive:
$12167 (23^3), 12168 (2^3 \times 3^2 \times 13^2)$

Find the $11^{th}$ pair (m,m+1) of consecutive pure powerful number - (12167, 12168) being the 1st

[My timing: < 30 sec]

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