what is an abundant number
http://www.google.com/search?hl=en&rlz=1G1GGLQ_ENUS308&defl=en&q=define:Abundant+number&sa=X&ei=PZKOTPCZIsGqlAf239XmAg&ved=0CBIQkAE
It is a number n whose sum of divisors, σ, exceeds 2 times the number itself.
That is to say:
&sigma(n)>2n
Example: 24 is an abundant number.
Ref: see
http://en.wikipedia.org/wiki/Abundant_number
An abundant number is a positive integer for which the sum of its proper divisors (excluding itself) is greater than the number itself.
To determine if a number is abundant, you need to find its proper divisors and then calculate their sum. If the sum is greater than the number, then it is considered an abundant number.
Here's a step-by-step explanation of how to determine if a number is abundant:
1. Start with a positive integer, let's call it 'n'.
2. Find all the divisors of 'n' that are less than 'n'. These are the proper divisors of 'n'.
- To find the divisors, you can divide 'n' by each number less than 'n' and check if the remainder is 0.
3. Calculate the sum of the proper divisors.
4. Compare the sum with 'n':
- If the sum is greater than 'n', then 'n' is an abundant number.
- If the sum is less than or equal to 'n', then 'n' is not an abundant number.
For example, let's use the number 12:
- The divisors of 12 are 1, 2, 3, 4, 6.
- The sum of these divisors is 1 + 2 + 3 + 4 + 6 = 16.
- Since 16 is greater than 12, we can conclude that 12 is an abundant number.