On Certain Sums Related to the Largest Odd Divisor

TL;DR

This paper investigates finite sums connected to the largest odd divisor, deriving precise bounds through simple methods and recurrence relations, contributing to number theory understanding.

Contribution

It introduces new bounds for sums related to the largest odd divisor using straightforward techniques and recurrence relations.

Findings

Established sharp upper bounds for the sums.

Derived sharp lower bounds for the sums.

Utilized simple ideas and recurrence relations for proofs.

Abstract

In this paper, we consider certain finite sums related to the "largest odd divisor", and we obtain, using simple ideas and recurrence relations, sharp upper and lower bounds for these sums.