iterated sum of divisors function

The iterated sum of divisors function σk(n) is ak in the recurrence relation a0=n and ai=σ(ai-1) for i>0, where σ(x) is the sum of divisors function.

Since n itself is included in the set of its divisorsMathworldPlanetmathPlanetmath, the sequenceMathworldPlanetmath 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 (σk(n))1k as k approaches infinityMathworldPlanetmathPlanetmath.


  • 1 R. K. Guy, Unsolved Problems in Number TheoryMathworldPlanetmathPlanetmath 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