Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# The Order of Euler’s Totient Function

Version 1 : Received: 18 July 2021 / Approved: 20 July 2021 / Online: 20 July 2021 (09:26:33 CEST)
Version 2 : Received: 17 August 2021 / Approved: 17 August 2021 / Online: 17 August 2021 (08:22:04 CEST)

How to cite: Cox, D.; Ghosh, S.; Sultanow, E. The Order of Euler’s Totient Function. Preprints 2021, 2021070428 (doi: 10.20944/preprints202107.0428.v1). Cox, D.; Ghosh, S.; Sultanow, E. The Order of Euler’s Totient Function. Preprints 2021, 2021070428 (doi: 10.20944/preprints202107.0428.v1).

## Abstract

The Mobius function is commonly used to define Euler’s totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) is used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function). Analogues of the product formula for the totient function are introduced. An analogue of the summatory totient function with many additive properties is introduced.

## Keywords

Mobius function; Mangoldt function; summatory totient function

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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