kb/data/en.wikipedia.org/wiki/Table_of_divisors-0.md

title	chunk	source	category	tags	date_saved	instance
Table of divisors	1/1	https://en.wikipedia.org/wiki/Table_of_divisors	reference	science, encyclopedia	2026-05-05T08:19:15.893082+00:00	kb-cron

The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which ⁠n/m⁠ is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since ⁠21/7⁠ = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n, then so is −m. The tables below only list positive divisors.

== Key to the tables == d(n) is the number of the positive divisors of n, including 1 and n itself σ(n) is the sum of the positive divisors of n, including 1 and n itself s(n) is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n a deficient number is greater than the sum of its proper divisors; that is, s(n) < n a perfect number equals the sum of its proper divisors; that is, s(n) = n an abundant number is lesser than the sum of its proper divisors; that is, s(n) > n a highly abundant number has a sum of positive divisors that is greater than any lesser number; that is, σ(n) > σ(m) for every positive integer m < n. Counterintuitively, the first seven highly abundant numbers (as well as the ninth) are not abundant numbers. a prime number has only 1 and itself as divisors; that is, d(n) = 2 a composite number has more than just 1 and itself as divisors; that is, d(n) > 2 a highly composite number has a number of positive divisors that is greater than any lesser number; that is, d(n) > d(m) for every positive integer m < n. Counterintuitively, the first two highly composite numbers are not composite numbers. a superior highly composite number has a ratio between its number of divisors and itself raised to some positive power that equals or is greater than the ratio of any other number; that is, there exists some ε such that

          d
          (
          n
          )
        
        
          n
          
            ε
          
        
      
    
    ≥
    
      
        
          d
          (
          m
          )
        
        
          m
          
            ε
          
        
      
    
  

{\textstyle {\frac {d(n)}{n^{\varepsilon }}}\geq {\frac {d(m)}{m^{\varepsilon }}}}

for every other positive integer m a primitive abundant number is an abundant number whose proper divisors are all deficient numbers a weird number is a number that is abundant but not semiperfect; that is, no subset of the proper divisors of n sum to n

== 1 to 100 ==

== 101 to 200 ==

== 201 to 300 ==

== 301 to 400 ==

== 401 to 500 ==

== 501 to 600 ==

== 601 to 700 ==

== 701 to 800 ==

== 801 to 900 ==

== 901 to 1000 ==

== Sortable 1-1000 ==

== See also == List of prime numbers Table of prime factors

== External links == OEIS sequence A027750 (Triangle read by rows in which row n lists the divisors of n)