Divisor summatory function

The summatory function, with leading terms removed, for $x<10^{4}$

The summatory function, with leading terms removed, for $x<10^{7}$

The summatory function, with leading terms removed, for $x<10^{7}$ , graphed as a distribution or histogram. The vertical scale is not constant left to right; click on image for a detailed description.

In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic behaviour of the Riemann zeta function. The various studies of the behaviour of the divisor function are sometimes called divisor problems.