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### Defining Kinds of Numbers

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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

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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/
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Associated Topics:
High School Number Theory
High School Sets