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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 = ∞?

Erdős Problems records this as disproved (Lean).

No Repository has ruled on it here.

How far the record reaches4 of 6 stages
  1. Sourceerdos-problems
  2. StatementRetained
  3. Formal5 retained
  4. Resolutiondisproved (Lean)
  5. WorkNone recorded
  6. DecisionNone here
  7. The questionNot reached
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Number Theory576
Erdős problem 321accepted
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