Explicit estimates of the weighted sum $S(x)={\sum }_{n\le x}(-2{)}^{\hat{I}\text{c◯}(n)}\log (\frac{x}{n}).$

Riddhi Manna

We study the oscillatory arithmetic function $(-2{)}^{\hat{I}\text{c◯}(n)}$, where $\hat{I}\text{c◯}(n)$ counts the number of prime factors of $n$, with multiplicity. Sun conjectured a bound on its partial sums…