A053727 - cp's OEIS frontend

A053727 Triangle T(n,k) = Sum_{d|gcd(n,k)} mu(d)*C(n/d,k/d) (n >= 1, 1 <= k <= n).

n	a(n)
1	1
2	2
3	0
4	3
5	3
6	0
7	4
8	4
9	4
10	0
11	5
12	10
13	10
14	5
15	0
16	6
17	12
18	18
19	12
20	6
21	0
22	7
23	21
24	35
25	35
26	21
27	7
28	0
29	8
30	24
31	56
32	64
33	56
34	24
35	8
36	0
37	9
38	36
39	81
40	126
41	126
42	81
43	36
44	9
45	0
46	10
47	40
48	120
49	200
50	250
51	200
52	120
53	40
54	10
55	0
56	11
57	55
58	165
59	330
60	462
61	462
62	330
63	165
64	55
65	11
66	0
67	12
68	60

[1, 2, 0, 3, 3, 0, 4, 4, 4, 0, 5, 10, 10, 5, 0, 6, 12, 18, 12, 6, 0, 7, 21, 35, 35, 21, 7, 0, 8, 24, 56, 64, 56, 24, 8, 0, 9, 36, 81, 126, 126, 81, 36, 9, 0, 10, 40, 120, 200, 250, 200, 120, 40, 10, 0, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 0, 12, 60]

cp's OEIS Frontend

A053727 Triangle T(n,k) = Sum_{d|gcd(n,k)} mu(d)*C(n/d,k/d) (n >= 1, 1 <= k <= n).

Table of values

List of values

n	a(n)
1	1
2	2
3	0
4	3
5	3
6	0
7	4
8	4
9	4
10	0
11	5
12	10
13	10
14	5
15	0
16	6
17	12
18	18
19	12
20	6
21	0
22	7
23	21
24	35
25	35
26	21
27	7
28	0
29	8
30	24
31	56
32	64
33	56
34	24
35	8
36	0
37	9
38	36
39	81
40	126
41	126
42	81
43	36
44	9
45	0
46	10
47	40
48	120
49	200
50	250
51	200
52	120
53	40
54	10
55	0
56	11
57	55
58	165
59	330
60	462
61	462
62	330
63	165
64	55
65	11
66	0
67	12
68	60

n	a(n)
1	1
2	2
3	0
4	3
5	3
6	0
7	4
8	4
9	4
10	0
11	5
12	10
13	10
14	5
15	0
16	6
17	12
18	18
19	12
20	6
21	0
22	7
23	21
24	35
25	35
26	21
27	7
28	0
29	8
30	24
31	56
32	64
33	56
34	24
35	8
36	0
37	9
38	36
39	81
40	126
41	126
42	81
43	36
44	9
45	0
46	10
47	40
48	120
49	200
50	250
51	200
52	120
53	40
54	10
55	0
56	11
57	55
58	165
59	330
60	462
61	462
62	330
63	165
64	55
65	11
66	0
67	12
68	60

n	a(n)
1	1
2	2
3	0
4	3
5	3
6	0
7	4
8	4
9	4
10	0
11	5
12	10
13	10
14	5
15	0
16	6
17	12
18	18
19	12
20	6
21	0
22	7
23	21
24	35
25	35
26	21
27	7
28	0
29	8
30	24
31	56
32	64
33	56
34	24
35	8
36	0
37	9
38	36
39	81
40	126
41	126
42	81
43	36
44	9
45	0
46	10
47	40
48	120
49	200
50	250
51	200
52	120
53	40
54	10
55	0
56	11
57	55
58	165
59	330
60	462
61	462
62	330
63	165
64	55
65	11
66	0
67	12
68	60