Year: 2025
Type: preprint
Abstract: In this article, we present relations for the Euler totient function $φ(n)$ and the number of divisors $τ(n)$ in terms of finite sums of integer parts of rational numbers or greatest common divisors of pairs of integers. Some of the formulas are obtained using a relation due to Menon and the connections with the Pillai arithmetic function are outlined. The reported expressions may be useful to derive new bounds for the usual arithmetical functions.
Source: arXiv (Cornell University)
Author: Pain, Jean-Christophe
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6929512133
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