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Erdős problem 1192

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Does there exist, for all r≥2r\geq 2, a basis AA of order rr (so that fr(n)>0f_r(n)>0 for all large nn) such that ∑n≤xfr(n)2≪x\sum_{n\leq x}f_r(n)^2 \ll x for all xx?

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Problem row
sha256:6eb42bb97c7df7ec98f81065f4ab7c248bc76ad00c734a4f5b1b3450523e417f
Metadata
sha256:997665bd8e420d5a983c76e3b66a4f672a11b875a6c2e7da2ab4469655bca54e
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:c0a306735c24fb1cf95c67c8d0bb4842901c5752687ffb8b1ca185f128b2fc43
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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