User:Virginia-American/Sandbox/table/Ramanujan Sum
Ramanujan Sum cs(n)
|
n
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
24
|
25
|
26
|
27
|
28
|
29
|
30
|
s
|
1
|
1
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1
|
2
|
−1
|
1
|
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1
|
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1
|
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1
|
3
|
−1 |
−1
|
2
|
−1 |
−1 |
2
|
−1 |
−1 |
2 |
−1 |
−1 |
2
|
−1 |
−1 |
2 |
−1 |
−1 |
2
|
−1 |
−1 |
2 |
−1 |
−1 |
2
|
−1 |
−1 |
2 |
−1 |
−1 |
2
|
4
|
0 |
−2 |
0
|
2
|
0 |
−2 |
0 |
2 |
0 |
−2
|
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
−2
|
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
−2
|
5
|
−1 |
−1 |
−1 |
−1 |
4
|
−1 |
−1 |
−1 |
−1 |
4
|
−1 |
−1 |
−1 |
−1 |
4
|
−1 |
−1 |
−1 |
−1 |
4
|
−1 |
−1 |
−1 |
−1 |
4
|
−1 |
−1 |
−1 |
−1 |
4
|
6
|
1 |
−1 |
−2 |
−1 |
1 |
2
|
1 |
−1 |
−2 |
−1 |
1 |
2
|
1 |
−1 |
−2 |
−1 |
1 |
2
|
1 |
−1 |
−2 |
−1 |
1 |
2
|
1 |
−1 |
−2 |
−1 |
1 |
2
|
7
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
6
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
6
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
6
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
6
|
−1 |
−1
|
8
|
0 |
0 |
0 |
−4 |
0 |
0 |
0 |
4
|
0 |
0 |
0 |
−4 |
0 |
0 |
0 |
4
|
0 |
0 |
0 |
−4 |
0 |
0 |
0 |
4
|
0 |
0 |
0 |
−4 |
0 |
0
|
9
|
0 |
0 |
−3 |
0 |
0 |
−3 |
0 |
0 |
6
|
0 |
0 |
−3 |
0 |
0 |
−3 |
0 |
0 |
6
|
0 |
0 |
−3 |
0 |
0 |
−3 |
0 |
0 |
6
|
0 |
0 |
−3
|
10
|
1 |
−1 |
1 |
−1 |
−4 |
−1 |
1 |
−1 |
1 |
4
|
1 |
−1 |
1 |
−1 |
−4 |
−1 |
1 |
−1 |
1 |
4
|
1 |
−1 |
1 |
−1 |
−4 |
−1 |
1 |
−1 |
1 |
4
|
11
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
10
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
10
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1
|
12
|
0 |
2 |
0 |
−2 |
0 |
−4 |
0 |
−2 |
0 |
2 |
0 |
4
|
0 |
2 |
0 |
−2 |
0 |
−4 |
0 |
−2 |
0 |
2 |
0 |
4
|
0 |
2 |
0 |
−2 |
0 |
−4
|
13
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
12
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
12
|
−1 |
−1 |
−1 |
−1
|
14
|
1 |
−1 |
1 |
−1 |
1 |
−1 |
−6 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
6
|
1 |
−1 |
1 |
−1 |
1 |
−1 |
−6 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
6
|
1 |
−1
|
15
|
1 |
1 |
−2 |
1 |
−4 |
−2 |
1 |
1 |
−2 |
−4 |
1 |
−2 |
1 |
1 |
8
|
1 |
1 |
−2 |
1 |
−4 |
−2 |
1 |
1 |
−2 |
−4 |
1 |
−2 |
1 |
1 |
8
|
16
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
−8 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
8
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
−8 |
0 |
0 |
0 |
0 |
0 |
0
|
17
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
16
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1
|
18
|
0 |
0 |
3 |
0 |
0 |
−3 |
0 |
0 |
−6 |
0 |
0 |
−3 |
0 |
0 |
3 |
0 |
0 |
6
|
0 |
0 |
3 |
0 |
0 |
−3 |
0 |
0 |
−6 |
0 |
0 |
−3
|
19
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
18
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1
|
20
|
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
−8
|
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
8
|
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
−8
|
21
|
1 |
1 |
−2 |
1 |
1 |
−2 |
−6 |
1 |
−2 |
1 |
1 |
−2 |
1 |
−6 |
−2 |
1 |
1 |
−2 |
1 |
1 |
12
|
1 |
1 |
−2 |
1 |
1 |
−2 |
−6 |
1 |
−2
|
22
|
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
−10
|
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
10
|
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1
|
23
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
22
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1
|
24
|
0 |
0 |
0 |
4
|
0 |
0 |
0 |
−4
|
0 |
0 |
0 |
−8
|
0 |
0 |
0 |
−4
|
0 |
0 |
0 |
4
|
0 |
0 |
0 |
8
|
0 |
0 |
0 |
4
|
0 |
0
|
25
|
0 |
0 |
0 |
0 |
−5
|
0 |
0 |
0 |
0 |
−5
|
0 |
0 |
0 |
0 |
−5
|
0 |
0 |
0 |
0 |
−5
|
0 |
0 |
0 |
0 |
20
|
0 |
0 |
0 |
0 |
−5
|
26
|
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
−12
|
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
−1 |
12
|
1 |
−1 |
1 |
−1
|
27
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
−9
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
−9
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
18
|
0 |
0 |
0
|
28
|
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
−12
|
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
−2 |
0 |
2 |
0 |
12
|
0 |
2
|
29
|
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
−1 |
28
|
−1
|
30
|
−1 |
1 |
2 |
1 |
4 |
−2 |
1 |
1 |
2 |
−4 |
−1 |
−2 |
−1 |
1 |
−8
|
1 |
−1 |
−2 |
−1 |
−4 |
2 |
1 |
−1 |
−2 |
4 |
1 |
2 |
1 |
−1 |
8
|