Input a number to check if it is abundant; define a range to generate all abundant numbers in the range.
An abundant number, also called an excessive number, is a positive integer whose proper divisors (excluding itself) sum to a value greater than the number itself. For example: 12 is an abundant number because its divisors (1, 2, 3, 4, 6) sum to 16, which is greater than 12.
Solution:
1. Find divisors:
The proper divisors of 25 are 1 and 5.
2. Sum of divisors:
1 + 5 = 6
3. Check Result:
6 < 25
Conclusion: 25 is not an abundant number, it's a deficient number.
Solution:
1. Find divisors:
The proper divisors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, and 248.
2. Sum of divisors:
1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496
3. Check Result:
496 = 496
Conclusion: 496 is not an abundant number; it is a perfect number.
Solution:
1. Find divisors:
The proper divisors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, and 500.
2. Sum of divisors:
1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 125 + 200 + 250 + 500 = 1340
3. Check Result:
1340 > 1000
Conclusion: 1000 is an abundant number.