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 Powerful and consecutive (Posted on 2010-08-09)
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!!

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): Too many? | Comment 9 of 16 |
(In reply to re: Too many? by Charlie)

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.
 Posted by ed bottemiller on 2010-08-09 14:42:16

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