{3,3,3,3,3,3} is a set of six integers such that the sum of the squares of the reciprocals totals 2/3.
(1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 = 2/3

Does there exist a set of integers with fewer than 6 members whose sum of the squares of the reciprocals totals 2/3?

Problem inspired by Find the triplets