Erdős problem 1064 · problems.science

Let $ϕ(n)$ be the Euler's totient function, then the $n$ satisfies $ϕ(n)>ϕ(n - ϕ(n))$ have asymptotic density 1. Reference: [LuPo02] Luca, Florian and Pomerance, Carl, On some problems of {M}\polhk akowski-{S}chinzel and {E}rdős concerning the arithmetical functions { $\phi$ } and { $\sigma$ }. Colloq. Math.

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FormalConjectures/ErdosProblems/

1064.lean

Retained formal statement2 of 3

For any function $f(n)=o(n)$ , we have $\phi(n)>\phi(n-\phi(n))+f(n)$ for almost all $n$ . Reference: [LuPo02] Luca, Florian and Pomerance, Carl, On some problems of {M}\polhk akowski-{S}chinzel and {E}rdős concerning the arithmetical functions { $\phi$ } and { $\sigma$ }. Colloq. Math. (2002), 111--130.

FormalConjectures/ErdosProblems/1064.leanErdos1064.erdos_1064.variants.general_function2 linesExact file

1∀ (f : ℕ → ℕ),2  ((fun n => ↑(f n)) =o[Filter.atTop] fun n => ↑n) → {n | (n - n.totient).totient + f n < n.totient}.HasDensity 1

SolvedStatement only, no proof

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