A345000 - cp's OEIS frontend

A345000 a(n) = gcd(A003415(n), A003415(A276086(n))), where A003415(n) is the arithmetic derivative of n, and A276086(n) gives the prime product form of primorial base expansion of n.

n	a(n)
0	0
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	4
9	1
10	1
11	1
12	2
13	1
14	1
15	1
16	16
17	1
18	3
19	1
20	2
21	5
22	1
23	1
24	4
25	5
26	5
27	1
28	2
29	1
30	1
31	1
32	10
33	1
34	1
35	3
36	12
37	1
38	1
39	1
40	2
41	1
42	1
43	1
44	4
45	1
46	5
47	1
48	2
49	1
50	5
51	5
52	4
53	1
54	3
55	1
56	2
57	1
58	1
59	1
60	2
61	1
62	1
63	1
64	12
65	3
66	1
67	1
68	2
69	1
70	1
71	1
72	12
73	1
74	1
75	55
76	10
77	3
78	1
79	1
80	16
81	1
82	1
83	1
84	2
85	1
86	5
87	1
88	140
89	1
90	3
91	1
92	16
93	1
94	49
95	3
96	2
97	1
98	7
99	1
100	28
101	1
102	7
103	1
104	2
105	1

[0, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 16, 1, 3, 1, 2, 5, 1, 1, 4, 5, 5, 1, 2, 1, 1, 1, 10, 1, 1, 3, 12, 1, 1, 1, 2, 1, 1, 1, 4, 1, 5, 1, 2, 1, 5, 5, 4, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 12, 3, 1, 1, 2, 1, 1, 1, 12, 1, 1, 55, 10, 3, 1, 1, 16, 1, 1, 1, 2, 1, 5, 1, 140, 1, 3, 1, 16, 1, 49, 3, 2, 1, 7, 1, 28, 1, 7, 1, 2, 1]

cp's OEIS Frontend

A345000 a(n) = gcd(A003415(n), A003415(A276086(n))), where A003415(n) is the arithmetic derivative of n, and A276086(n) gives the prime product form of primorial base expansion of n.

Table of values

List of values

n	a(n)
0	0
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	4
9	1
10	1
11	1
12	2
13	1
14	1
15	1
16	16
17	1
18	3
19	1
20	2
21	5
22	1
23	1
24	4
25	5
26	5
27	1
28	2
29	1
30	1
31	1
32	10
33	1
34	1
35	3
36	12
37	1
38	1
39	1
40	2
41	1
42	1
43	1
44	4
45	1
46	5
47	1
48	2
49	1
50	5
51	5
52	4
53	1
54	3
55	1
56	2
57	1
58	1
59	1
60	2
61	1
62	1
63	1
64	12
65	3
66	1
67	1
68	2
69	1
70	1
71	1
72	12
73	1
74	1
75	55
76	10
77	3
78	1
79	1
80	16
81	1
82	1
83	1
84	2
85	1
86	5
87	1
88	140
89	1
90	3
91	1
92	16
93	1
94	49
95	3
96	2
97	1
98	7
99	1
100	28
101	1
102	7
103	1
104	2
105	1

n	a(n)
0	0
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	4
9	1
10	1
11	1
12	2
13	1
14	1
15	1
16	16
17	1
18	3
19	1
20	2
21	5
22	1
23	1
24	4
25	5
26	5
27	1
28	2
29	1
30	1
31	1
32	10
33	1
34	1
35	3
36	12
37	1
38	1
39	1
40	2
41	1
42	1
43	1
44	4
45	1
46	5
47	1
48	2
49	1
50	5
51	5
52	4
53	1
54	3
55	1
56	2
57	1
58	1
59	1
60	2
61	1
62	1
63	1
64	12
65	3
66	1
67	1
68	2
69	1
70	1
71	1
72	12
73	1
74	1
75	55
76	10
77	3
78	1
79	1
80	16
81	1
82	1
83	1
84	2
85	1
86	5
87	1
88	140
89	1
90	3
91	1
92	16
93	1
94	49
95	3
96	2
97	1
98	7
99	1
100	28
101	1
102	7
103	1
104	2
105	1

n	a(n)
0	0
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	4
9	1
10	1
11	1
12	2
13	1
14	1
15	1
16	16
17	1
18	3
19	1
20	2
21	5
22	1
23	1
24	4
25	5
26	5
27	1
28	2
29	1
30	1
31	1
32	10
33	1
34	1
35	3
36	12
37	1
38	1
39	1
40	2
41	1
42	1
43	1
44	4
45	1
46	5
47	1
48	2
49	1
50	5
51	5
52	4
53	1
54	3
55	1
56	2
57	1
58	1
59	1
60	2
61	1
62	1
63	1
64	12
65	3
66	1
67	1
68	2
69	1
70	1
71	1
72	12
73	1
74	1
75	55
76	10
77	3
78	1
79	1
80	16
81	1
82	1
83	1
84	2
85	1
86	5
87	1
88	140
89	1
90	3
91	1
92	16
93	1
94	49
95	3
96	2
97	1
98	7
99	1
100	28
101	1
102	7
103	1
104	2
105	1