Divisor Function - Table of Values

Table of Values

n Divisors σ0(n) σ1(n) s(n) = σ1(n) − n Comment
1 1 1 1 0 square number: σ0(n) is odd; power of 2: s(n) = n − 1 (almost-perfect)
2 1,2 2 3 1 Prime: σ1(n) = 1+n so s(n) =1
3 1,3 2 4 1 Prime: σ1(n) = 1+n so s(n) =1
4 1,2,4 3 7 3 square number: σ0(n) is odd; power of 2: s(n) = n − 1 (almost-perfect)
5 1,5 2 6 1 Prime: σ1(n) = 1+n so s(n) =1
6 1,2,3,6 4 12 6 first perfect number: s(n) = n
7 1,7 2 8 1 Prime: σ1(n) = 1+n so s(n) =1
8 1,2,4,8 4 15 7 power of 2: s(n) = n − 1 (almost-perfect)
9 1,3,9 3 13 4 square number: σ0(n) is odd
10 1,2,5,10 4 18 8
11 1,11 2 12 1 Prime: σ1(n) = 1+n so s(n) =1
12 1,2,3,4,6,12 6 28 16 first abundant number: s(n) > n
13 1,13 2 14 1 Prime: σ1(n) = 1+n so s(n) =1
14 1,2,7,14 4 24 10
15 1,3,5,15 4 24 9
16 1,2,4,8,16 5 31 15 square number: σ0(n) is odd; power of 2: s(n) = n − 1 (almost-perfect)

The cases x=2, x=3 and so on are tabulated in  A001157,  A001158,  A001159,  A001160,  A013954,  A013955 ...

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