A373365 - cp's OEIS frontend

A373365 a(n) = gcd(A001414(n), A064097(n)), where A001414 is the sum of prime factors with repetition, and A064097 is a quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1.

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

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

cp's OEIS Frontend

A373365 a(n) = gcd(A001414(n), A064097(n)), where A001414 is the sum of prime factors with repetition, and A064097 is a quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1.

Table of values

List of values

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

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

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