Math Goodies is a free math help portal for students, teachers, and parents.
|
Interactive Math Goodies Software

testing left nav
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
 All Forums  Homework Help Forums  Miscellaneous Math Topics  help with math notation needed -abundant numbers New Topic  Reply to Topic  Printer Friendly
Author  Topic

USA
635 Posts

 Posted - 05/08/2013 :  14:42:12 I have a colleague who is trying to convert the text notation into math notation with mathtype for this articleCan 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.```

TchrWill

USA
80 Posts

 Posted - 05/26/2013 :  19:18:11 quote:Originally posted by AdminI have a colleague who is trying to convert the text notation into math notation with mathtype for this articleCan 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.....3Sa(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...8etc.
Topic
 New Topic  Reply to Topic  Printer Friendly Jump To: Select Forum New Visitor Forum       Testing Forum Homework Help Forums       Basic Math and Pre-Algebra       Algebra       Geometry and Trigonometry       Pre-Calculus and Calculus       Probability and Statistics       Standardized Test Preparation Help       Miscellaneous Math Topics Educator Forum       Teacher Talk Parent Forum       Parent's Place  -------------------- Home Active Topics Frequently Asked Questions Member Information Search Page
 Math Forums @ Math Goodies © 2000-2004 Snitz Communications