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 ...
Read more about this topic: Divisor Function
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