Enter a number to check if it is almost perfect. Or input a start and end range to generate all almost perfect numbers within that range.
An almost perfect number is a positive integer where the sum of all its proper divisors (excluding itself) equals the number itself minus one. In other words, the sum of its proper divisors plus 1 equals the number itself. Almost perfect numbers are a unique subset of numbers in number theory.
To check if a number is almost perfect, follow these steps:
Solution:
1. Find the sum of proper divisors:
Proper divisors of 20 are 1, 2, 4, 5, and 10. Their sum is: \(1 + 2 + 4 + 5 + 10 = 22\).
2. Compare the sum:
\(22 > 20 - 1\).
Result: 20 is not an almost perfect number.
Solution:
1. Find the sum of proper divisors:
Proper divisors of 32 are 1, 2, 4, 8, and 16. Their sum is: \(1 + 2 + 4 + 8 + 16 = 31\).
2. Compare the sum:
\(31 = 32 - 1\).
Result: 32 is an almost perfect number.