Input a number to determine if it is deficient; or define a range to generate all deficient numbers within it.
A deficient number is the opposite of an abundant number. It is a positive integer whose proper divisors (excluding itself) sum to a value less than the number itself. For example: 8 is a deficient number because its divisors (1, 2, 4) sum to 7, which is less than 8.
Solution:
1. Find divisors:
The proper divisors of 15 are 1, 3, and 5.
2. Sum of divisors:
1 + 3 + 5 = 9
3. Check the Result:
9 < 15
Conclusion: Since 9 < 15, 15 is a deficient number.
Solution:
1. Find divisors:
The proper divisors of 28 are 1, 2, 4, 7, and 14.
2. Sum of divisors:
1 + 2 + 4 + 7 + 14 = 28
Conclusion: 28 is a perfect number, not a deficient number.
Solution:
1. Find divisors:
The proper divisors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48.
2. Sum of divisors:
1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 = 156
3. Check the Result:
156 > 96
Conclusion: Since 156 > 96, 96 is not a deficient number, it is an abundant number.