Defining Kinds of NumbersDate: 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/ |
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