Input a number to check if it's semiperfect, or input a range to generate all semiperfect numbers within that range.
Semiperfect Number Check or Generate
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What Is a Semiperfect Number?
A semiperfect number, also known as a pseudoperfect number, is a positive integer that equals the sum of some (but not necessarily all) of its proper divisors. Unlike perfect numbers, semiperfect numbers require only a subset of their divisors to sum up to the original number. For example: 12 is a semiperfect number because its divisors are 1, 2, 3, 4, 6, and 12. Among these, the subset 1 + 2 + 3 + 6 = 12.
How to Determine if a Number Is Semiperfect
Find the Divisors: Identify all proper divisors of the number (excluding the number itself). For example, the divisors of 12 are 1, 2, 3, and 4.
Calculate Subset Sums: Explore various combinations of these divisors to check if any subset sums up to the original number.
Check the Result: If at least one subset of divisors adds up to the original number, it is semiperfect. If no subset equals the number, it is not semiperfect.