Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# Euler's Totient Function, the Mangoldt Function, and a Sequence of Mertens Function Values

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. Euler's Totient Function, the Mangoldt Function, and a Sequence of Mertens Function Values. Preprints 2021, 2021070428 (doi: 10.20944/preprints202107.0428.v2). Cox, D.; Ghosh, S.; Sultanow, E. Euler's Totient Function, the Mangoldt Function, and a Sequence of Mertens Function Values. Preprints 2021, 2021070428 (doi: 10.20944/preprints202107.0428.v2).

## 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) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

## Keywords

Mobius function; Mangoldt function; summatory totient function

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comment 1
Commenter: Sourangshu Ghosh
Commenter's Conflict of Interests: Author
Comment: Additional new properties of Mertens Function are discovered and discussed.
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