Statements (34)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appearsIn |
gptkb:Euclid's_Elements
Nicomachus's Introduction to Arithmetic |
| gptkbp:category |
gptkb:Number_theory
|
| gptkbp:defines |
A positive integer that is equal to the sum of its proper positive divisors, excluding itself
|
| gptkbp:etymology |
From Latin 'perfectus', meaning complete
|
| gptkbp:first_known_perfect_number |
6
|
| gptkbp:form |
If 2^p − 1 is prime, then 2^{p−1}(2^p − 1) is a perfect number
|
| gptkbp:fourth_known_perfect_number |
8128
|
| gptkbp:has_divisor_function |
σ(n) = 2n for perfect number n
|
| gptkbp:has_divisors_sum_property |
Sum of divisors equals twice the number
|
| gptkbp:has_OEIS_sequence |
A000396
|
| gptkbp:hasProperty |
Abundant number
Centered nonagonal number Harmonic divisor number Hexagonal number Triangular number |
| https://www.w3.org/2000/01/rdf-schema#label |
Perfect Number
|
| gptkbp:open_question |
Existence of odd perfect numbers is unknown
|
| gptkbp:property |
All known perfect numbers are even
|
| gptkbp:relatedConcept |
Mersenne prime
Abundant number Amicable numbers Deficient number Sociable numbers |
| gptkbp:relatedTo |
Mersenne prime
|
| gptkbp:second_known_perfect_number |
28
|
| gptkbp:sequence |
6, 28, 496, 8128, 33550336, ...
|
| gptkbp:studiedBy |
gptkb:Euclid
gptkb:Euler |
| gptkbp:symbol |
No standard symbol
|
| gptkbp:third_known_perfect_number |
496
|
| gptkbp:bfsParent |
gptkb:Lee_Yo-won
|
| gptkbp:bfsLayer |
7
|