A234514 - cp's OEIS frontend

A234514 Number of ways to write n = k + m with k > 0 and m > 0 such that p = k + phi(m)/2 and q(p) + 1 are both prime, where phi(.) is Euler's totient function, and q(.) is the strict partition function (A000009).

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

[0, 0, 0, 1, 2, 2, 1, 1, 1, 0, 1, 0, 2, 2, 2, 3, 4, 2, 4, 2, 3, 3, 3, 2, 2, 3, 1, 4, 2, 1, 4, 2, 4, 2, 5, 3, 4, 1, 5, 6, 4, 2, 5, 5, 5, 3, 5, 4, 6, 3, 5, 7, 10, 2, 4, 5, 6, 5, 5, 2, 3, 5, 6, 6, 4, 2, 5, 3, 7, 4, 5, 3, 8, 7, 2, 5, 9, 3, 3, 2, 9, 9, 6, 6, 7, 6, 9, 4, 7, 4, 10, 8, 6, 11, 11, 4, 6, 4, 9, 7]

cp's OEIS Frontend

A234514 Number of ways to write n = k + m with k > 0 and m > 0 such that p = k + phi(m)/2 and q(p) + 1 are both prime, where phi(.) is Euler's totient function, and q(.) is the strict partition function (A000009).

Table of values

List of values

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

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

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