Erdős problem 489

If $A$ is a forbidden-divisor set with $|A \cap [1,x]| = o(\sqrt{x})$ and $B = \{b_1 < b_2 < \cdots\}$ the sifted set, must $x^{-1} \sum_{b_i < x} (b_{i+1} - b_i)^2$ converge to a finite limit?

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If $A$ is a forbidden-divisor set with $|A \cap [1,x]| = o(\sqrt{x})$ and $B = \{b_1 < b_2 < \cdots\}$ the sifted set, must $x^{-1} \sum_{b_i < x} (b_{i+1} - b_i)^2$ converge to a finite limit?

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