Exercise · ZW-PERFECT-NUMBER-003 · ★★☆ Intermediate
Which of these values of \(n\) satisfies the definition of a perfect number?
Choose one option.
Show answer
- B. 6
Explanation
The number 6 is the only one in the list whose proper divisors sum to itself. The number 15 sums to 9, 24 sums to 36, and 20 sums to 22.
Review the concept: Perfect number
A perfect number is a positive integer \(n\) equal to the sum of its proper divisors, those smaller than \(n\); with the divisor-sum function \(\sigma\), the sum of all its divisors is twice \(n\).
\[\sigma(n)=2n\]
More practice problems: perfect number
- ZW-PERFECT-NUMBER-001 Which of these numbers is perfect?
- ZW-PERFECT-NUMBER-002 What is the second smallest perfect number?
- ZW-PERFECT-NUMBER-004 How much do the proper divisors of 28 sum to?
- ZW-PERFECT-NUMBER-005 Which of these statements defines a perfect number n?
- ZW-PERFECT-NUMBER-006 Compute the sum of the proper divisors of 12 and state whether 12 is perfect.
- ZW-PERFECT-NUMBER-007 What is the third smallest perfect number?
- ZW-PERFECT-NUMBER-008 If 2^p-1 is prime with p=7, which perfect number does Euclid's formula give?
- ZW-PERFECT-NUMBER-009 Which of the following statements is false?