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!!

8,288,675,9800 ....

a sequence of p.n.  such that p.n.+1 is a p.n as well. 

 

It is easy to see that this sequence is infinite:
if n is in the sequence, so is 4n*(n+1).

 

 [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 16 2009]

Posted by Ady TZIDON on 2010-08-09 14:45:22