Approximation of the Multiplication Table Function

Abstract

In this paper, considering the concept of Universal Multiplication Table, we show that for every $n\ge 2$, the inequality: $$ M(n)=#\{ij|1\leq i,j\leq n\}\geq\frac{n^2}{\mathfrak{N}(n^2)}, $$ holds true with: $$\mathfrak{N}(n)=n^{\frac{\log 2}{\log \log n}(1+\frac{387}{200\log \log n})}.$$

5 pages