The proper divisors of a positive integer are all of the divisors less than the integer you started with. A semiperfect number is the sum of some of its proper divisors. If a semiperfect number is the sum of all of its proper divisors, it is called a perfect number . The proper divisors of the first number in the group add up to the second number, the proper divisors of the second number add up to the third number, and so on. The sum of the proper divisors of the last number in the group is equal to the first number.
Sociable numbers tend to be quite large, so they are hard to find without using a computer.
The number of evenly spaced dots needed to make a square is a square number. This is just one kind of polygonal number . The same site proves that there are an infinite amount of numbers that are both square and triangular . Back to Top Tetrahedral Numbers Tetrahedral numbers are one kind of figurate number . They are found by counting the number of evenly spaced points needed to build a tetrahedron.