Erdős problem 50

Schoenberg [Sch38] proved that the asymptotic distribution function of $\varphi(n)/n$ exists. That is, for any $c \in [0, 1]$ , the proportion of integers $n \le N$ satisfying $\varphi(n)/n < c$ approaches a limit as $N \to \infty$ . This limit function is the cumulative distribution function of the values of $\varphi(n)/n$ .

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FormalConjectures/ErdosProblems/

50.lean

Retained formal statement2 of 3

Schoenberg [Sch38] proved that the asymptotic distribution function of $\varphi(n)/n$ exists. That is, for any $c \in [0, 1]$ , the proportion of integers $n \le N$ satisfying $\varphi(n)/n < c$ approaches a limit as $N \to \infty$ . This limit function is the cumulative distribution function of the values of $\varphi(n)/n$ .

FormalConjectures/ErdosProblems/50.leanErdos50.erdos_50_schoenberg1 lineExact file

1∃ f, Erdos50.IsDistributionOfPhiRatio f

SolvedStatement only, no proof