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.