Each of P, Q, R, S and T are positive integers with P < Q < R < S < T. Determine the maximum value of the following expression.

[P, Q] ^-1 + [Q, R] ^-1 + [R, S] ^-1 + [S, T] ^-1

Note: [x, y] represents the LCM of x and y.

(In reply to Extension (and ideas) by Gamer)

I agree completely with Gamer's points:

a) a series of any length would be more interesting
b) switching any term of 1,2,4,8,16 ... to a larger number results in a smaller result, and doesn't work.
c) We still need to prove that switching a term of 1,2,4,8,16 ... to a small number also results in a smaller result.  This hasn't been done yet.

Posted by Steve Herman on 2008-10-05 11:05:39