A234567 - cp's OEIS frontend

A234567 Number of ways to write n = k + m with k > 0 and m > 0 such that p = phi(k) + phi(m)/2 + 1 and P(p-1) are both prime, where phi(.) is Euler's totient function and P(.) is the partition function (A000041).

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

[0, 0, 0, 1, 2, 1, 1, 3, 2, 2, 3, 2, 4, 2, 4, 4, 2, 4, 3, 5, 1, 3, 2, 3, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 1, 2, 1, 1, 2, 1, 2, 3, 2, 8, 2, 1, 2, 2, 3, 3, 1, 2, 7, 0, 2, 3, 3, 4, 5, 7, 3, 4, 1, 9, 1, 4, 3, 1, 2]

cp's OEIS Frontend

A234567 Number of ways to write n = k + m with k > 0 and m > 0 such that p = phi(k) + phi(m)/2 + 1 and P(p-1) are both prime, where phi(.) is Euler's totient function and P(.) is the partition function (A000041).

Table of values

List of values

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

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

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