Powerful numbers (4,8,9,16,25,27... )are defined as follows: if a prime p divides n then p^{2} 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: An interesting remark ***** Spoiler by Daniel)

1.Of course, it is obvious. That's why the sentence begins:...it is **easy** to see...etc

2.It is not "my discovery" - I've quoted the source.

3. There is a small typo in the 4th row of your post, which should read: . " .now it remains to show that 4n(n+1)__+1__

is also a p.n. "

You may still edit it.