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!!

(In reply to Question by Brian Smith)

Yes, it does.

A powerfol number may be expressed by a^2*b^3,
a  & b integers not necessarily primes.

The basic definition covers all your samples.

The unique representation of P.N. i.e. 
(p1)^a1*(p2)^a2*...  (pk)^ak  should display no a=1, no power less than 2.

Posted by Ady TZIDON on 2010-08-09 14:21:18