Abstract
Properties of divisor functions sigma(k)(n), defined as sums of k-th powers of all divisors of n, are studied through the analysis of Ramanujan's differential equations. This system of three differential equations is singular at x = 0. Solution techniques suitable to tackle this singularity are developed and the problem is transformed into an analysis of a dynamical system. Number theoretical consequences of the presented dynamical system analysis are then discussed, including recursive formulas for divisor functions.