A349394 - cp's OEIS frontend

A349394 a(p^e) = p^(e-1) for prime powers, a(n) = 0 for all other n; Dirichlet convolution of A003415 (arithmetic derivative of n) with A055615 (Dirichlet inverse of n).

n	a(n)
1	0
2	1
3	1
4	2
5	1
6	0
7	1
8	4
9	3
10	0
11	1
12	0
13	1
14	0
15	0
16	8
17	1
18	0
19	1
20	0
21	0
22	0
23	1
24	0
25	5
26	0
27	9
28	0
29	1
30	0
31	1
32	16
33	0
34	0
35	0
36	0
37	1
38	0
39	0
40	0
41	1
42	0
43	1
44	0
45	0
46	0
47	1
48	0
49	7
50	0
51	0
52	0
53	1
54	0
55	0
56	0
57	0
58	0
59	1
60	0
61	1
62	0
63	0
64	32
65	0
66	0
67	1
68	0
69	0
70	0
71	1
72	0
73	1
74	0
75	0
76	0
77	0
78	0
79	1
80	0
81	27
82	0
83	1
84	0
85	0
86	0
87	0
88	0
89	1
90	0
91	0
92	0
93	0
94	0
95	0
96	0
97	1
98	0
99	0
100	0
101	1
102	0
103	1
104	0
105	0

[0, 1, 1, 2, 1, 0, 1, 4, 3, 0, 1, 0, 1, 0, 0, 8, 1, 0, 1, 0, 0, 0, 1, 0, 5, 0, 9, 0, 1, 0, 1, 16, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 7, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 32, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 27, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]

cp's OEIS Frontend

A349394 a(p^e) = p^(e-1) for prime powers, a(n) = 0 for all other n; Dirichlet convolution of A003415 (arithmetic derivative of n) with A055615 (Dirichlet inverse of n).

Table of values

List of values

n	a(n)
1	0
2	1
3	1
4	2
5	1
6	0
7	1
8	4
9	3
10	0
11	1
12	0
13	1
14	0
15	0
16	8
17	1
18	0
19	1
20	0
21	0
22	0
23	1
24	0
25	5
26	0
27	9
28	0
29	1
30	0
31	1
32	16
33	0
34	0
35	0
36	0
37	1
38	0
39	0
40	0
41	1
42	0
43	1
44	0
45	0
46	0
47	1
48	0
49	7
50	0
51	0
52	0
53	1
54	0
55	0
56	0
57	0
58	0
59	1
60	0
61	1
62	0
63	0
64	32
65	0
66	0
67	1
68	0
69	0
70	0
71	1
72	0
73	1
74	0
75	0
76	0
77	0
78	0
79	1
80	0
81	27
82	0
83	1
84	0
85	0
86	0
87	0
88	0
89	1
90	0
91	0
92	0
93	0
94	0
95	0
96	0
97	1
98	0
99	0
100	0
101	1
102	0
103	1
104	0
105	0

n	a(n)
1	0
2	1
3	1
4	2
5	1
6	0
7	1
8	4
9	3
10	0
11	1
12	0
13	1
14	0
15	0
16	8
17	1
18	0
19	1
20	0
21	0
22	0
23	1
24	0
25	5
26	0
27	9
28	0
29	1
30	0
31	1
32	16
33	0
34	0
35	0
36	0
37	1
38	0
39	0
40	0
41	1
42	0
43	1
44	0
45	0
46	0
47	1
48	0
49	7
50	0
51	0
52	0
53	1
54	0
55	0
56	0
57	0
58	0
59	1
60	0
61	1
62	0
63	0
64	32
65	0
66	0
67	1
68	0
69	0
70	0
71	1
72	0
73	1
74	0
75	0
76	0
77	0
78	0
79	1
80	0
81	27
82	0
83	1
84	0
85	0
86	0
87	0
88	0
89	1
90	0
91	0
92	0
93	0
94	0
95	0
96	0
97	1
98	0
99	0
100	0
101	1
102	0
103	1
104	0
105	0

n	a(n)
1	0
2	1
3	1
4	2
5	1
6	0
7	1
8	4
9	3
10	0
11	1
12	0
13	1
14	0
15	0
16	8
17	1
18	0
19	1
20	0
21	0
22	0
23	1
24	0
25	5
26	0
27	9
28	0
29	1
30	0
31	1
32	16
33	0
34	0
35	0
36	0
37	1
38	0
39	0
40	0
41	1
42	0
43	1
44	0
45	0
46	0
47	1
48	0
49	7
50	0
51	0
52	0
53	1
54	0
55	0
56	0
57	0
58	0
59	1
60	0
61	1
62	0
63	0
64	32
65	0
66	0
67	1
68	0
69	0
70	0
71	1
72	0
73	1
74	0
75	0
76	0
77	0
78	0
79	1
80	0
81	27
82	0
83	1
84	0
85	0
86	0
87	0
88	0
89	1
90	0
91	0
92	0
93	0
94	0
95	0
96	0
97	1
98	0
99	0
100	0
101	1
102	0
103	1
104	0
105	0