Key To The Tables
- d(n) is the number of positive divisors of n, including 1 and n itself
- σ(n) is the sum of all the positive divisors of n, including 1 and n itself
- s(n) is the sum of the proper divisors of n, which does not include n itself; that is, s(n) = σ(n) − n
- a perfect number equals the sum of its proper divisors; that is, s(n) = n; the only perfect numbers between 1 and 1000 are 6, 28 and 496
- amicable numbers and sociable numbers are numbers where the sum of their proper divisors form a cycle; the only examples below 1000 are 220 and 284
- a deficient number is greater than the sum of its proper divisors; that is, s(n) < n
- an abundant number is less than the sum of its proper divisors; that is, s(n) > n
- a prime number has only 1 and itself as divisors; that is, d(n) = 2. Prime numbers are always deficient as s(n)=1
Read more about this topic: Table Of Divisors
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