Defining Kinds of Numbers

Date: 03/21/97 at 17:08:35
From: LINDA BUNTING
Subject: Kinds of Numbers

What is the definition of:

 1. Perfect numbers
 2. Deficient numbers
 3. Square numbers
 4. Abundant numbers
 5. Amicable numbers
 6. Triangular numbers

Thank you for your time!

Date: 03/21/97 at 17:39:52
From: Doctor Steven
Subject: Re: Kinds of Numbers


1. Perfect number - number whose divisors (except itself) add up to 
   the number itself.

   6 is a perfect number: 1 + 2 + 3 = 6
  28 is a perfect number: 1 + 2 + 4 + 7 + 14 = 28


2. Deficient number - number whose divisors (except itself) add up to 
   less than the number itself.

   9 is a deficient number: 1 + 3 = 4
  21 is a deficient number: 1 + 3 + 7 = 11
  16 is a deficient number: 1 + 2 + 4 + 8 = 15


3. Square number - a number that can be formed by counting the number 
   of objects used in making a square.

           o      1 is a square number
                  
           oo
           oo     4 is a square number

           ooo
           ooo
           ooo    9 is a square number


4. Abundant number - a number whose divisor (except itself) add up to 
   more than the number itself.

  12 is an abundant number: 1 + 2 + 3 + 4 + 6 = 16
  18 is an abundant number: 1 + 2 + 3 + 6 + 9 = 21

                     
5. Amicable numbers - a pair (or more) of numbers, M and N, such that 
   the sum of the divisors of M (except M) adds to N. And the sum of 
   the divisors of N (except N) adds to M.  (For more than two numbers 
   we get a chain effect. Say we have three amicable numbers, M, N, P: 
   Then sum of divisors of M add to N, sum of divisors of N add to P, 
   sum of divisors of P add to M.)


6. Triangular number - a number that can be formed by counting the 
   number of object used in making a triangle.

               o      1 is a triangular number

               o
              o o     3 is a triangular number

               o
              o o
             o o o    6 is a triangular number


It might be interesting to find a formula for finding square and 
triangular numbers. These two types of numbers come from a class of 
numbers called figurate numbers. Other types of figurate numbers 
include pentagonal numbers and hexagonal numbers. These are a fairly 
interesting set of numbers.  Enjoy.

-Doctor Steven,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/