Sociable Number Checker

Sociable Number Checker is a free online tool used to check if the number is a sociable number.

Sociable numbers are numbers with aliquot sums forming a cyclic sequence beginning and ending with the same number. The aliquot sum of a number is the sum of all the positive integer divisors other than the number itself.

Sociable numbers are considered generalized versions of perfect numbers and amicable numbers. Paul Poulet, the Belgian mathematician, was the first to discover a sociable number. A sociable sequence is formed when each number in the sequence is the sum of the proper divisors of its predecessor in the sequence. Such a sequence is called sociable if the sequence becomes cyclic, returning to its starting point.

For example, is 1210 a sociable number?

First, find all proper factors of 1210. They are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605.

Second, calculate the sum of proper factors of 1210.

1 + 2 + 5 + 10 + 11 + 22 + 55 + 110 + 121 + 242 + 605 = 1184

Repeat the above two steps with 1184, the sum of proper divisors of 1184 is

1 + 2 + 4 + 8 + 16 + 32 + 37 + 74 + 148 + 296 + 592 = 1210

back to 1210. So, 1210 is a sociable number.

The procedure to use the sociable number checker is as follows: