testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
Username:
Password:
Save Password
Forgot your Password?

 All Forums
 Homework Help Forums
 Miscellaneous Math Topics
 help with math notation needed -abundant numbers
 New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic  

Admin
Forum Admin

USA
635 Posts

Posted - 05/08/2013 :  14:42:12  Show Profile  Reply with Quote
I have a colleague who is trying to convert the text notation into math notation with mathtype for this article

Can someone use the math symbols in the forums to convert the math notation below?

Abundant numbers are part of the family of numbers that are either deficient, perfect, or abundant.

Abundant numbers are numbers where the sum, Sa(N), of its aliquot parts/divisors is more than the number itself Sa(N) > N or S(N) > 2N. (In the language of the Greek mathematicians, the divisors of a number N were defined as any whole number smaller than N that, when divided into N, produced whole numbers. The factors/divisors of a number N, less the number itself, are referred to as the aliquot parts, aliquot divisors, or proper divisors, of the number.) Equivalently, N is also abundant if the sum, S(N), of "all" its divisors is greater than 2N. 

 

From the following list

N-->.......1..2..3..4..5...6....7...8....9..10..11..12..13..14..15..16..17..18..19...20..21..22..23..24

Sa(N)-->1..1..1..3..1...6....1...7....4...8....1...16...1...10...9...15...1....21...1...22..11..12...1...36

S(N)-->  1..3..4..7..6..12...8..15..13.18..12..28..14..22..24..31..18...39..20..42..32..36..24..60

 

..........................................12,18,20, and 24 are abundant.

 

It can be readily seen that using the aliquot parts summation, sa(24) = 1+2+3+4+6+8+12 = 36 > N = 24 while s(24) = 1+2+3+4+6+8+12+24 = 60 > 2N = 48, making 24 abundant using either definition.
Go to Top of Page

TchrWill
Advanced Member

USA
80 Posts

Posted - 05/26/2013 :  19:18:11  Show Profile  Reply with Quote
quote:
Originally posted by Admin

I have a colleague who is trying to convert the text notation into math notation with mathtype for this article

Can someone use the math symbols in the forums to convert the math notation below?

Abundant numbers are part of the family of numbers that are either deficient, perfect, or abundant.

Abundant numbers are numbers where the sum, Sa(N), of its aliquot parts/divisors is more than the number itself Sa(N) > N or S(N) > 2N. (In the language of the Greek mathematicians, the divisors of a number N were defined as any whole number smaller than N that, when divided into N, produced whole numbers. The factors/divisors of a number N, less the number itself, are referred to as the aliquot parts, aliquot divisors, or proper divisors, of the number.) Equivalently, N is also abundant if the sum, S(N), of "all" its divisors is greater than 2N. 

 

From the following list

N-->.......1..2..3..4..5...6....7...8....9..10..11..12..13..14..15..16..17..18..19...20..21..22..23..24

Sa(N)-->1..1..1..3..1...6....1...7....4...8....1...16...1...10...9...15...1....21...1...22..11..12...1...36

S(N)-->  1..3..4..7..6..12...8..15..13.18..12..28..14..22..24..31..18...39..20..42..32..36..24..60

 

..........................................12,18,20, and 24 are abundant.

 

It can be readily seen that using the aliquot parts summation, sa(24) = 1+2+3+4+6+8+12 = 36 > N = 24 while s(24) = 1+2+3+4+6+8+12+24 = 60 > 2N = 48, making 24 abundant using either definition.




In the given table, N = the number, "a" = the number of aliquot parts, "n" = the specific aliquot part, and Sa(N) = the sum of the aliquot parts of the number N.

...N..1...2...3...4...5...6...7...8...9...10...11...12...13...14
...a..1...1...1...2...1...3...1...3...2....3....1...5....1.....3
Sa(N).1...1...1...3...1...6...1...7...4....8....1...16...1....10

...N...a...n
...1...1...1
...2...1...1
...3...2...1
...4...2...3
...5...1...1
...6...3...6
...7...1...1
...8...3...7
...9...2...4
..10...3...8
etc.
Go to Top of Page
  Previous Topic Topic Next Topic  
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.07 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 21 May 2014