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 statement3 of 3

Let $ϕ(n)$ be the Euler's totient function, there exist infinitely many $n$ such that $ϕ(n)< ϕ(n - ϕ(n))$ Reference: [GLW01] Grytczuk, A. and Luca, F. and Wójtowicz, M., A conjecture of {E}rdős concerning inequalities for the {E}uler totient function.

FormalConjectures/ErdosProblems/1064.leanErdos1064.erdos_1064.variants.k21 lineExact file

1{n | n.totient < (n - n.totient).totient}.Infinite

SolvedStatement only, no proof

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