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Erdős problem 897

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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sha256:4410ae8dd40f931eb0a8eed88127b135f1a1ded8cbc4255dedaf030973d15359
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2415f78e850aeee50afdca525c6f2e0ea606f207
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