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 re: Too many?
Charlie, as I read the problem, 24 would be an example, since it is divisible by 2 (a prime) and 4 (the square of that prime). I admit that the wording was not clear to me; the "must also" is vague. I took it to mean that a "powerful number" must be divisible by the square of at least one prime. As a "definition" it is not clear the status of primes themselves -- which are divisible by themselves, but not by their squares. All of the sample cases given were powers of a single prime, so little guidance.