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Erdős problem 897

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Let f(n)f(n) be an additive function (so that f(ab)=f(a)+f(b)f(ab)=f(a)+f(b) if (a,b)=1(a,b)=1 such that lim sup⁡p,kf(pk)/log⁡(pk)=∞\limsup_{p,k} f(p^k) / \log(p^k) = ∞. Is it true that lim sup⁡n(f(n+1)−f(n))/log⁡n=∞\limsup_n (f(n+1)−f(n))/ \log n = ∞?

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Problem row
sha256:4410ae8dd40f931eb0a8eed88127b135f1a1ded8cbc4255dedaf030973d15359
Metadata
sha256:334925719cf781c577a9763bd32e8fb64bcdb7156fe8fd09056ada7e42cb79f0
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:391ec2cff0b4e46ff336b472d4317421e852af82223b1e9b260569cace6c91e5
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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