A349163 - cp's OEIS frontend

A349163 a(n) = A064989(gcd(sigma(n), A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes, while A064989 shifts it back towards smaller primes, and sigma is the sum of divisors function.

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

[1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 10, 1, 2, 1, 6, 1, 2, 3, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 10, 1, 2, 1, 1, 5, 2, 1, 4, 1, 2, 1, 6, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 11, 5, 1, 2, 1, 2, 1]

cp's OEIS Frontend

A349163 a(n) = A064989(gcd(sigma(n), A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes, while A064989 shifts it back towards smaller primes, and sigma is the sum of divisors function.

Table of values

List of values

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

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

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