Quasiperfect number
Encyclopedia
In mathematics
, a quasiperfect number is a theoretical natural number
n for which the sum of all its divisor
s (the divisor function
σ(n)) is equal to 2n + 1. Quasiperfect numbers are abundant numbers.
No quasiperfect numbers have been found so far, but if a quasiperfect number exists, it must be an odd square number
greater than 1035 and have at least seven distinct prime factor
s.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a quasiperfect number is a theoretical natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
n for which the sum of all its divisor
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...
s (the divisor function
Divisor function
In mathematics, and specifically in number theory, a divisor function is an arithmetical function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer. It appears in a number of remarkable identities, including relationships...
σ(n)) is equal to 2n + 1. Quasiperfect numbers are abundant numbers.
No quasiperfect numbers have been found so far, but if a quasiperfect number exists, it must be an odd square number
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...
greater than 1035 and have at least seven distinct prime factor
Prime factor
In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. A prime factor can be visualized by understanding Euclid's...
s.