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Erdős problem 66

Is there and A⊂NA \subset \mathbb{N} is such that lim⁡n→∞1A∗1A(n)log⁡n\lim_{n\to \infty}\frac{1_A\ast 1_A(n)}{\log n} exists and is ≠0\ne 0?

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sha256:f7063fcafa625f7b6be999af882529f7b72287a67490ba37f16f84798015ccdc
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sha256:787fa6ce4aa403508ba969672f2b5840743ea36395494c8f287e557d78e39a25
Observation
sha256:8c823d621b7e1256c8e47c60a5f1c54c016a5507e6f27b2bab537f6f5f232067
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sha256:b38bdf23094bebaa922c2fe7b3c90ec309964d18853e973d00c2570406d1c473
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sha256:c9d14c459c518937e758918b5897dc3b22f1a55f07739afe99502f5b046c907a
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2415f78e850aeee50afdca525c6f2e0ea606f207
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