The wolframalpha page on the divisor function, http://mathworld.wolfram.com/DivisorFunction.html
Lists the asymptotic estimate,
However, I have tried to get the same estimate on my own by interchanging the summation on the left hand side and using the dirichlet hyperbola method.
Doing this the best estimate I can seem to get is,
Were non 'elementary' techniques used to obtain the first asymptotic? Or is it a typo?