iterated sum of divisors function

The iterated sum of divisors function ${\sigma }^k(n)$ is $a_k$ in the recurrence relation $a_0=n$ and $a_i=\sigma (a_{i-1})$ for $i>0$, where $\sigma (x)$ is the sum of divisors function.

Since $n$ itself is included in the set of its divisors, the sequence generated by repeated iterations is an increasing sequence (that is, in ascending order). For example, iterating the sum of divisors function for $n=2$ gives the sequence 2, 3, 4, 7, 8, 15, etc. Erdős conjectured that there is a limit for ${({\sigma }^k(n))}^{\frac{1}{k}}$ as $k$ approaches infinity.

Title	iterated sum of divisors function
Canonical name	IteratedSumOfDivisorsFunction
Date of creation	2013-03-22 17:03:36
Last modified on	2013-03-22 17:03:36
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A25