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.