Number theory · Oct 6, 2026

An asymptotic formula for the number of totients

Gives an asymptotic equivalent for the number V(x)V(x) of distinct totient values up to x, with a positive bounded phase-dependent factor determined by convergent arithmetic approximations. In particular, V(cx)/V(x)→cV(cx)/V(x)\to c for every fixed c > 0, answering Erdős and Hall’s scaling question.

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