A054533 - cp's OEIS frontend

A054533 Triangular array giving Ramanujan sum T(n,k) = c_n(k) = Sum_{m=1..n, (m,n)=1} exp(2 Pi i m k / n) for n >= 1 and 1 <= k <= n.

n	a(n)
1	1
2	-1
3	1
4	-1
5	-1
6	2
7	0
8	-2
9	0
10	2
11	-1
12	-1
13	-1
14	-1
15	4
16	1
17	-1
18	-2
19	-1
20	1
21	2
22	-1
23	-1
24	-1
25	-1
26	-1
27	-1
28	6
29	0
30	0
31	0
32	-4
33	0
34	0
35	0
36	4
37	0
38	0
39	-3
40	0
41	0
42	-3
43	0
44	0
45	6
46	1
47	-1
48	1
49	-1
50	-4
51	-1
52	1
53	-1
54	1
55	4
56	-1
57	-1
58	-1
59	-1
60	-1
61	-1
62	-1
63	-1
64	-1
65	-1
66	10
67	0
68	2
69	0
70	-2
71	0
72	-4
73	0
74	-2
75	0
76	2
77	0
78	4
79	-1
80	-1
81	-1
82	-1
83	-1
84	-1
85	-1
86	-1
87	-1
88	-1
89	-1
90	-1
91	12
92	1

[1, -1, 1, -1, -1, 2, 0, -2, 0, 2, -1, -1, -1, -1, 4, 1, -1, -2, -1, 1, 2, -1, -1, -1, -1, -1, -1, 6, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -3, 0, 0, -3, 0, 0, 6, 1, -1, 1, -1, -4, -1, 1, -1, 1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 0, 2, 0, -2, 0, -4, 0, -2, 0, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 12, 1]

cp's OEIS Frontend

A054533 Triangular array giving Ramanujan sum T(n,k) = c_n(k) = Sum_{m=1..n, (m,n)=1} exp(2 Pi i m k / n) for n >= 1 and 1 <= k <= n.

Table of values

List of values

n	a(n)
1	1
2	-1
3	1
4	-1
5	-1
6	2
7	0
8	-2
9	0
10	2
11	-1
12	-1
13	-1
14	-1
15	4
16	1
17	-1
18	-2
19	-1
20	1
21	2
22	-1
23	-1
24	-1
25	-1
26	-1
27	-1
28	6
29	0
30	0
31	0
32	-4
33	0
34	0
35	0
36	4
37	0
38	0
39	-3
40	0
41	0
42	-3
43	0
44	0
45	6
46	1
47	-1
48	1
49	-1
50	-4
51	-1
52	1
53	-1
54	1
55	4
56	-1
57	-1
58	-1
59	-1
60	-1
61	-1
62	-1
63	-1
64	-1
65	-1
66	10
67	0
68	2
69	0
70	-2
71	0
72	-4
73	0
74	-2
75	0
76	2
77	0
78	4
79	-1
80	-1
81	-1
82	-1
83	-1
84	-1
85	-1
86	-1
87	-1
88	-1
89	-1
90	-1
91	12
92	1

n	a(n)
1	1
2	-1
3	1
4	-1
5	-1
6	2
7	0
8	-2
9	0
10	2
11	-1
12	-1
13	-1
14	-1
15	4
16	1
17	-1
18	-2
19	-1
20	1
21	2
22	-1
23	-1
24	-1
25	-1
26	-1
27	-1
28	6
29	0
30	0
31	0
32	-4
33	0
34	0
35	0
36	4
37	0
38	0
39	-3
40	0
41	0
42	-3
43	0
44	0
45	6
46	1
47	-1
48	1
49	-1
50	-4
51	-1
52	1
53	-1
54	1
55	4
56	-1
57	-1
58	-1
59	-1
60	-1
61	-1
62	-1
63	-1
64	-1
65	-1
66	10
67	0
68	2
69	0
70	-2
71	0
72	-4
73	0
74	-2
75	0
76	2
77	0
78	4
79	-1
80	-1
81	-1
82	-1
83	-1
84	-1
85	-1
86	-1
87	-1
88	-1
89	-1
90	-1
91	12
92	1

n	a(n)
1	1
2	-1
3	1
4	-1
5	-1
6	2
7	0
8	-2
9	0
10	2
11	-1
12	-1
13	-1
14	-1
15	4
16	1
17	-1
18	-2
19	-1
20	1
21	2
22	-1
23	-1
24	-1
25	-1
26	-1
27	-1
28	6
29	0
30	0
31	0
32	-4
33	0
34	0
35	0
36	4
37	0
38	0
39	-3
40	0
41	0
42	-3
43	0
44	0
45	6
46	1
47	-1
48	1
49	-1
50	-4
51	-1
52	1
53	-1
54	1
55	4
56	-1
57	-1
58	-1
59	-1
60	-1
61	-1
62	-1
63	-1
64	-1
65	-1
66	10
67	0
68	2
69	0
70	-2
71	0
72	-4
73	0
74	-2
75	0
76	2
77	0
78	4
79	-1
80	-1
81	-1
82	-1
83	-1
84	-1
85	-1
86	-1
87	-1
88	-1
89	-1
90	-1
91	12
92	1