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iterated sum of divisors function
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(Definition)
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The iterated sum of divisors function
 is  in the recurrence relation  and
 for  , where  is the sum of divisors function.
Since  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  gives the sequence 2, 3, 4, 7, 8, 15, etc. Erdős conjectured that there is a limit for
 as  approaches infinity.
- 1
- R. K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag 2004: B9
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"iterated sum of divisors function" is owned by CompositeFan.
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(view preamble)
Cross-references: infinity, limit, ascending order, increasing, iterations, generated by, sequence, divisors, sum of divisors function, recurrence relation
There are 2 references to this entry.
This is version 1 of iterated sum of divisors function, born on 2007-05-09.
Object id is 9351, canonical name is IteratedSumOfDivisorsFunction.
Accessed 933 times total.
Classification:
| AMS MSC: | 11A25 (Number theory :: Elementary number theory :: Arithmetic functions; related numbers; inversion formulas) |
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Pending Errata and Addenda
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