95=5×19→(1+5+19)=25=5×5→(1+5)=6→6→6→….
What has happened here is that although 95 is not itselfa sociable number, its aliquot sequence eventually hits a sociable number(or more precisely in this case, the perfect number 6)and then goes into a cycle.
There is conceivably one possibility remaining, that being that the aliquot sequence of a number never hits a prime nor a sociable number, in which case the sequence must be an unending series of different numbers, none of which are either prime or sociable. Is this possible? Surprisingly, no one knows. What is more surprising is that there are small numbers whose aliquot sequence remain unknown(and thereby remain candidates for having such an infinite aliquot sequence). The first of these mysterious numbers is276, whose sequence begins: