A054535 - cp's OEIS frontend

A054535 Square array giving Ramanujan sum T(n,k) = c_n(k) = Sum_{m=1..n, (m,n)=1} exp(2 Pi i m k / n), read by antidiagonals upwards (n >= 1, k >= 1).

n	a(n)
1	1
2	-1
3	1
4	-1
5	1
6	1
7	0
8	-1
9	-1
10	1
11	-1
12	-2
13	2
14	1
15	1
16	1
17	-1
18	0
19	-1
20	-1
21	1
22	-1
23	-1
24	-1
25	2
26	-1
27	1
28	1
29	0
30	-1
31	-2
32	-1
33	0
34	2
35	-1
36	1
37	0
38	0
39	-1
40	-1
41	4
42	-2
43	-1
44	1
45	1
46	1
47	0
48	0
49	-1
50	1
51	-1
52	0
53	-1
54	-1
55	1
56	-1
57	-1
58	-3
59	-4
60	-1
61	2
62	-1
63	2
64	2
65	1
66	1
67	0
68	-1
69	1
70	0
71	0
72	-1
73	1
74	-1
75	0
76	-1
77	-1
78	1
79	-1
80	2
81	-1
82	-1
83	0
84	0
85	6
86	-1
87	-1
88	-2
89	-1
90	1
91	1
92	1
93	-1

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

cp's OEIS Frontend

A054535 Square array giving Ramanujan sum T(n,k) = c_n(k) = Sum_{m=1..n, (m,n)=1} exp(2 Pi i m k / n), read by antidiagonals upwards (n >= 1, k >= 1).

Table of values

List of values

n	a(n)
1	1
2	-1
3	1
4	-1
5	1
6	1
7	0
8	-1
9	-1
10	1
11	-1
12	-2
13	2
14	1
15	1
16	1
17	-1
18	0
19	-1
20	-1
21	1
22	-1
23	-1
24	-1
25	2
26	-1
27	1
28	1
29	0
30	-1
31	-2
32	-1
33	0
34	2
35	-1
36	1
37	0
38	0
39	-1
40	-1
41	4
42	-2
43	-1
44	1
45	1
46	1
47	0
48	0
49	-1
50	1
51	-1
52	0
53	-1
54	-1
55	1
56	-1
57	-1
58	-3
59	-4
60	-1
61	2
62	-1
63	2
64	2
65	1
66	1
67	0
68	-1
69	1
70	0
71	0
72	-1
73	1
74	-1
75	0
76	-1
77	-1
78	1
79	-1
80	2
81	-1
82	-1
83	0
84	0
85	6
86	-1
87	-1
88	-2
89	-1
90	1
91	1
92	1
93	-1

n	a(n)
1	1
2	-1
3	1
4	-1
5	1
6	1
7	0
8	-1
9	-1
10	1
11	-1
12	-2
13	2
14	1
15	1
16	1
17	-1
18	0
19	-1
20	-1
21	1
22	-1
23	-1
24	-1
25	2
26	-1
27	1
28	1
29	0
30	-1
31	-2
32	-1
33	0
34	2
35	-1
36	1
37	0
38	0
39	-1
40	-1
41	4
42	-2
43	-1
44	1
45	1
46	1
47	0
48	0
49	-1
50	1
51	-1
52	0
53	-1
54	-1
55	1
56	-1
57	-1
58	-3
59	-4
60	-1
61	2
62	-1
63	2
64	2
65	1
66	1
67	0
68	-1
69	1
70	0
71	0
72	-1
73	1
74	-1
75	0
76	-1
77	-1
78	1
79	-1
80	2
81	-1
82	-1
83	0
84	0
85	6
86	-1
87	-1
88	-2
89	-1
90	1
91	1
92	1
93	-1

n	a(n)
1	1
2	-1
3	1
4	-1
5	1
6	1
7	0
8	-1
9	-1
10	1
11	-1
12	-2
13	2
14	1
15	1
16	1
17	-1
18	0
19	-1
20	-1
21	1
22	-1
23	-1
24	-1
25	2
26	-1
27	1
28	1
29	0
30	-1
31	-2
32	-1
33	0
34	2
35	-1
36	1
37	0
38	0
39	-1
40	-1
41	4
42	-2
43	-1
44	1
45	1
46	1
47	0
48	0
49	-1
50	1
51	-1
52	0
53	-1
54	-1
55	1
56	-1
57	-1
58	-3
59	-4
60	-1
61	2
62	-1
63	2
64	2
65	1
66	1
67	0
68	-1
69	1
70	0
71	0
72	-1
73	1
74	-1
75	0
76	-1
77	-1
78	1
79	-1
80	2
81	-1
82	-1
83	0
84	0
85	6
86	-1
87	-1
88	-2
89	-1
90	1
91	1
92	1
93	-1