Submitted:
18 July 2021
Posted:
20 July 2021
Read the latest preprint version here
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
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