FunWithNumbers (version 1.2)

aliquot: Generate the Aliquot Sequence.

Description

Each term in the aliquot sequence is generated by summing all proper divisors of the previous term. The value "1" is included in this collection of divisors. In number theory, aliquot is closely related to terms such as "sociable" and "amicable" numbers

Usage

aliquot(x, maxiter = 100)

Value

A list containing theseq, the sequence generated converged, a logical value indicating whether convergence (including cyclic) was reached. thecycle, the subset of theseq which is cyclic

Arguments

x

An integer , bigz integer, or character string representing an integer to start the desired sequence

maxiter

Set a limit on the number of terms to calculate. See Details for reasons why to do so.

Author

Carl Witthoft,

Details

While many aliquot sequences terminate in the values c(prime_number, 1, 0), many numbers drop into a short loop or a repeating value (perfect numbers do this). If the sequence repeats or terminates, the sequence is returned. If maxiter is reached, the output converged is set to FALSE and the sequence so far is returned.

Examples

aliquot(20)
# $theseq
# Big Integer ('bigz') object of length 7:
# [1] 20 22 14 10 8  7  1 
# $converged
# [1] TRUE
# $thecycle
# Big Integer ('bigz') :
# [1] 1
# (aliquot(1264460))
# $theseq
# Big Integer ('bigz') object of length 5:
# [1] 1264460 1547860 1727636 1305184 1264460
# $converged
# [1] TRUE
# $thecycle
# Big Integer ('bigz') object of length 5:
# [1] 1264460 1547860 1727636 1305184 1264460