A054534 - cp's OEIS frontend

A054534 Square array giving Ramanujan sum T(n,k) = c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2 Pi i m n / k), read by antidiagonals upwards (n >= 1, k >= 1).

n	a(n)
1	1
2	1
3	-1
4	1
5	1
6	-1
7	1
8	-1
9	-1
10	0
11	1
12	1
13	2
14	-2
15	-1
16	1
17	-1
18	-1
19	0
20	-1
21	1
22	1
23	1
24	-1
25	2
26	-1
27	-1
28	-1
29	1
30	-1
31	2
32	0
33	-1
34	-2
35	-1
36	0
37	1
38	1
39	-1
40	-2
41	4
42	-1
43	-1
44	0
45	0
46	1
47	-1
48	-1
49	0
50	-1
51	1
52	-1
53	0
54	0
55	1
56	1
57	1
58	2
59	2
60	-1
61	2
62	-1
63	-4
64	-3
65	-1
66	-1
67	1
68	-1
69	-1
70	0
71	-1
72	1
73	-1
74	0
75	0
76	1
77	-1
78	0
79	1
80	1
81	-1
82	-2
83	-1
84	-1
85	6
86	0
87	0
88	-1
89	-1
90	2
91	-1
92	1
93	-1
94	2
95	0
96	4
97	-2
98	-1
99	0
100	-3
101	-4
102	-1
103	0
104	-1
105	1

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

cp's OEIS Frontend

A054534 Square array giving Ramanujan sum T(n,k) = c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2 Pi i m n / k), 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	1
8	-1
9	-1
10	0
11	1
12	1
13	2
14	-2
15	-1
16	1
17	-1
18	-1
19	0
20	-1
21	1
22	1
23	1
24	-1
25	2
26	-1
27	-1
28	-1
29	1
30	-1
31	2
32	0
33	-1
34	-2
35	-1
36	0
37	1
38	1
39	-1
40	-2
41	4
42	-1
43	-1
44	0
45	0
46	1
47	-1
48	-1
49	0
50	-1
51	1
52	-1
53	0
54	0
55	1
56	1
57	1
58	2
59	2
60	-1
61	2
62	-1
63	-4
64	-3
65	-1
66	-1
67	1
68	-1
69	-1
70	0
71	-1
72	1
73	-1
74	0
75	0
76	1
77	-1
78	0
79	1
80	1
81	-1
82	-2
83	-1
84	-1
85	6
86	0
87	0
88	-1
89	-1
90	2
91	-1
92	1
93	-1
94	2
95	0
96	4
97	-2
98	-1
99	0
100	-3
101	-4
102	-1
103	0
104	-1
105	1

n	a(n)
1	1
2	1
3	-1
4	1
5	1
6	-1
7	1
8	-1
9	-1
10	0
11	1
12	1
13	2
14	-2
15	-1
16	1
17	-1
18	-1
19	0
20	-1
21	1
22	1
23	1
24	-1
25	2
26	-1
27	-1
28	-1
29	1
30	-1
31	2
32	0
33	-1
34	-2
35	-1
36	0
37	1
38	1
39	-1
40	-2
41	4
42	-1
43	-1
44	0
45	0
46	1
47	-1
48	-1
49	0
50	-1
51	1
52	-1
53	0
54	0
55	1
56	1
57	1
58	2
59	2
60	-1
61	2
62	-1
63	-4
64	-3
65	-1
66	-1
67	1
68	-1
69	-1
70	0
71	-1
72	1
73	-1
74	0
75	0
76	1
77	-1
78	0
79	1
80	1
81	-1
82	-2
83	-1
84	-1
85	6
86	0
87	0
88	-1
89	-1
90	2
91	-1
92	1
93	-1
94	2
95	0
96	4
97	-2
98	-1
99	0
100	-3
101	-4
102	-1
103	0
104	-1
105	1

n	a(n)
1	1
2	1
3	-1
4	1
5	1
6	-1
7	1
8	-1
9	-1
10	0
11	1
12	1
13	2
14	-2
15	-1
16	1
17	-1
18	-1
19	0
20	-1
21	1
22	1
23	1
24	-1
25	2
26	-1
27	-1
28	-1
29	1
30	-1
31	2
32	0
33	-1
34	-2
35	-1
36	0
37	1
38	1
39	-1
40	-2
41	4
42	-1
43	-1
44	0
45	0
46	1
47	-1
48	-1
49	0
50	-1
51	1
52	-1
53	0
54	0
55	1
56	1
57	1
58	2
59	2
60	-1
61	2
62	-1
63	-4
64	-3
65	-1
66	-1
67	1
68	-1
69	-1
70	0
71	-1
72	1
73	-1
74	0
75	0
76	1
77	-1
78	0
79	1
80	1
81	-1
82	-2
83	-1
84	-1
85	6
86	0
87	0
88	-1
89	-1
90	2
91	-1
92	1
93	-1
94	2
95	0
96	4
97	-2
98	-1
99	0
100	-3
101	-4
102	-1
103	0
104	-1
105	1