Extremal estimates for strongly additive and strongly multiplicative arithmetic functions

TL;DR

This paper investigates extremal estimates for sums and products involving prime numbers, focusing on strongly additive and multiplicative arithmetic functions, providing new proofs and examples for these estimates.

Contribution

It introduces new extremal estimates for strongly additive and multiplicative functions, with proofs and illustrative examples, advancing understanding in this area.

Findings

Proved several assertions on sums and products of prime-related functions.

Established extremal bounds for strongly additive functions.

Provided examples illustrating the extremal estimates.

Abstract

The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for strongly additive and strongly multiplicative arithmetic functions. Several assertions on this topic are proved and examples are considered.