A235051 - cp's OEIS frontend

A235051 a(n) = |{0 < k < n-2: C(sigma(k) + phi(n-k)/2) - 1 is prime}|, where C(j) is the j-th Catalan number (A000108), sigma(k) is the sum of all positive divisors of k, and phi(.) is Euler's totient function.

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

[0, 0, 0, 0, 1, 2, 3, 4, 3, 5, 3, 4, 4, 4, 5, 3, 4, 4, 5, 3, 2, 1, 4, 2, 2, 2, 4, 2, 2, 2, 2, 4, 5, 1, 1, 1, 3, 1, 2, 2, 5, 1, 1, 3, 1, 2, 1, 2, 1, 4, 3, 3, 3, 1, 0, 0, 2, 2, 2, 1, 7, 1, 0, 4, 1, 3, 1, 1, 2, 2, 1, 7, 4, 4, 1, 3, 3, 2, 3, 4, 3, 1, 7, 1, 5, 2, 5, 1, 3, 3, 4, 5, 1, 4, 2, 3, 4, 6, 5, 3]

cp's OEIS Frontend

A235051 a(n) = |{0 < k < n-2: C(sigma(k) + phi(n-k)/2) - 1 is prime}|, where C(j) is the j-th Catalan number (A000108), sigma(k) is the sum of all positive divisors of k, and phi(.) is Euler's totient function.

Table of values

List of values

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

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

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