# Dirichlet's Divisor Function

We know that by Dirichlet's formula for the Divisor function $\displaystyle \sum\limits_{n \leq x} d(n) = x \log{x} + (2C-1)x + \mathcal{O}(\sqrt{x})$.

What is the best approximation available till date for the given formula. I know that finding the infimum of the $\mathcal{O}'s$ is an unsolved problem, but would like to see the closest approximation.

• This question was already asked on MO, I'll try to find it (and close yours afterwards :-( ). You are very-very curious! :-) Aug 2, 2010 at 10:01
• I don't know why should it stay open in this wrong form. ;-) BTW, all question lovers are advised to first visit the OEIS and Wikipedia, before posting their questions. You obviously missed this standard procedure... Aug 2, 2010 at 10:45
• Please make some effort to solve your own curiosity questions. Aug 3, 2010 at 11:45