A054532 - cp's OEIS frontend

A054532 Ramanujan sum T(n, k) = c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2Piimn / k), triangular array read by rows for n >= 1 and 1 <= k <= n.

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

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

cp's OEIS Frontend

A054532 Ramanujan sum T(n, k) = c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2Piimn / k), triangular array read by rows 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	1
8	1
9	-1
10	2
11	1
12	-1
13	-1
14	0
15	4
16	1
17	1
18	2
19	-2
20	-1
21	2
22	1
23	-1
24	-1
25	0
26	-1
27	1
28	6
29	1
30	1
31	-1
32	2
33	-1
34	-1
35	-1
36	4
37	1
38	-1
39	2
40	0
41	-1
42	-2
43	-1
44	0
45	6
46	1
47	1
48	-1
49	-2
50	4
51	-1
52	-1
53	0
54	0
55	4
56	1
57	-1
58	-1
59	0
60	-1
61	1
62	-1
63	0
64	0
65	1
66	10
67	1
68	1
69	2
70	2
71	-1
72	2
73	-1
74	-4
75	-3
76	-1
77	-1
78	4
79	1
80	-1
81	-1
82	0
83	-1
84	1
85	-1
86	0
87	0
88	1
89	-1
90	0
91	12
92	1

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

cp's OEIS Frontend

A054532 Ramanujan sum T(n, k) = c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2*Pi*i*m*n / k), triangular array read by rows for n >= 1 and 1 <= k <= n.

Table of values

List of values

A054532 Ramanujan sum T(n, k) = c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2Piimn / k), triangular array read by rows for n >= 1 and 1 <= k <= n.

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