The first two sociable sequences, or sociable chains, were discovered and named by the Belgian mathematician Paul Poulet in 1918.
If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number—for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6.
There are no known sociable numbers of order 3, and searches for them have been made up to
The aliquot sequence can be represented as a directed graph,
represent sociable numbers within the interval
Two special cases are loops that represent perfect numbers and cycles of length two that represent amicable pairs.
It is conjectured that as the number of sociable number cycles with length greater than 2 approaches infinity, the proportion of the sums of the sociable number cycles divisible by 10 approaches 1 (sequence A292217 in the OEIS).