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 help with math notation needed -abundant numbers

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T O P I C    R E V I E W
Admin 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 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.
1   L A T E S T    R E P L I E S    (Newest First)
TchrWill Posted - 05/26/2013 : 19:18:11
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.

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