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^{}.
References
- 1 R. K. Guy, Unsolved Problems in Number Theory^{} New York: Springer-Verlag 2004: B9
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 |