Powerful numbers (4,8,9,16,25,27... )are defined as follows: if a prime p divides n then p² must also divide n.
(8,9) is a couple of two consecutive numbers,both of them being powerful.
Find another pair(s) like that.

The more the merrier!!

Your example sequence has only perfect powers.  Does your definition of 'powerful numbers' include numbers like 36, 72, and 100, which are products of perfect powers?

Posted by Brian Smith on 2010-08-09 12:05:30