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
Famous quotes containing the words table and/or values:
“The newspaper is a Bible which we read every morning and every afternoon, standing and sitting, riding and walking. It is a Bible which every man carries in his pocket, which lies on every table and counter, and which the mail, and thousands of missionaries, are continually dispersing. It is, in short, the only book which America has printed, and which America reads. So wide is its influence.”
—Henry David Thoreau (1817–1862)
“[University students] hated the hypocrisy of adult society, the rigidity of its political institutions, the impersonality of its bureaucracies. They sought to create a society that places human values before materialistic ones, that has a little less head and a little more heart, that is dominated by self-interest and loves its neighbor more. And they were persuaded that group protest of a militant nature would advance those goals.”
—Muriel Beadle (b. 1915)