# The Distribution of Totients

@article{Ford1998TheDO,
title={The Distribution of Totients},
author={Kevin Ford},
journal={The Ramanujan Journal},
year={1998},
volume={2},
pages={67-151}
}
• K. Ford
• Published 1 March 1998
• Mathematics
• The Ramanujan Journal
AbstractThis paper is a comprehensive study of the set of totients, i.e., the set of values taken by Euler's φ-function. The main functions studied are V(x), the number of totients ≤x, A(m), the number of solutions of φ(x)=m (the “multiplicity” of m), and V_k(x), the number of m ≤ x with A(m)=k. The first of the main results of the paper is a determination of the true order ofV(x) . It is also shown that for each k ≥ 1, if there is a totient with multiplicity k then V_k(x) ≫ V(x). Sierpiński…
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