Erdős–Tenenbaum–Ford constant

The Erdős–Tenenbaum–Ford constant is a mathematical constant that appears in number theory. Named after mathematicians Paul Erdős, Gérald Tenenbaum, and Kevin Ford, it is defined as
 * $$\delta := 1 - \frac{1 + \log \log 2}{\log 2} = 0.0860713320\dots$$

where $$\log$$ is the natural logarithm.

Following up on earlier work by Tenenbaum, Ford used this constant in analyzing the number $$H(x,y,z)$$ of integers that are at most $$x$$ and that have a divisor in the range $$[y,z]$$.

Multiplication table problem
For each positive integer $$N$$, let $$M(N)$$ be the number of distinct integers in an $$N \times N$$ multiplication table. In 1960, Erdős studied the asymptotic behavior of $$M(N)$$ and proved that
 * $$M(N) = \frac{N^2}{(\log N)^{\delta + o(1)}},$$

as $$N \to +\infty$$.