Editing Sociable number (section)

== Searching for sociable numbers ==

The [[aliquot sequence]] can be represented as a [[directed graph]], <math>G_{n,s}</math>, for a given integer <math>n</math>, where <math>s(k)</math> denotes the
sum of the proper divisors of <math>k</math>.<ref>{{citation|title=Distributed cycle detection in large-scale sparse graphs|first1=Rodrigo Caetano|last1=Rocha|first2=Bhalchandra|last2=Thatte|year=2015|publisher=Simpósio Brasileiro de Pesquisa Operacional (SBPO)|doi=10.13140/RG.2.1.1233.8640}}</ref>
[[cycle (graph theory)|Cycles]] in <math>G_{n,s}</math> represent sociable numbers within the interval <math>[1,n]</math>. Two special cases are loops that represent [[perfect numbers]] and cycles of length two that represent [[amicable pairs]].