 In this case the probability that the gcd equals "d" is "d"−2/ζ(2), and since ζ(2) = π2/6 we have

This last summation is the harmonic series, which diverges.However, when "k" ≥ 3, the expected value is well-defined, and by the above argument, it is

For "k" = 3, this is approximately equal to 1.3684.For "k" = 4, it is approximately 1.1106.