Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 024-01. An asymptotic formula for the number of totients
Manuscript map · lines 2935–2944
OpenAI@2026-10-07#rem:oai-p-024-01
Authors: OpenAI. Family 024.
Title: An asymptotic formula for the number of totients.
Abstract: Let $V(x)$ count the distinct values of Euler's totient function up to x. We give an explicit asymptotic equivalent for $V(x)$. Its coefficient is a uniform limit of functions defined from finite arithmetic data. We also prove that $V(cx)/V(x){}to c$ as $x{}to{}infty$ for every fixed c > 0, answering a question of Erdős and Hall.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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