A349164 - cp's OEIS frontend

A349164 a(n) = A064989(A003961(n) / 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	1
3	3
4	4
5	5
6	3
7	7
8	4
9	9
10	5
11	11
12	12
13	13
14	7
15	15
16	16
17	17
18	9
19	19
20	2
21	21
22	11
23	23
24	4
25	25
26	13
27	9
28	28
29	29
30	15
31	31
32	8
33	33
34	17
35	35
36	36
37	37
38	19
39	39
40	10
41	41
42	21
43	43
44	22
45	45
46	23
47	47
48	48
49	49
50	25
51	51
52	52
53	53
54	9
55	55
56	28
57	19
58	29
59	59
60	6
61	61
62	31
63	63
64	64
65	13
66	33
67	67
68	17
69	69
70	35
71	71
72	12
73	73
74	37
75	75
76	76
77	77
78	39
79	79
80	40
81	81
82	41
83	83
84	84

[1, 1, 3, 4, 5, 3, 7, 4, 9, 5, 11, 12, 13, 7, 15, 16, 17, 9, 19, 2, 21, 11, 23, 4, 25, 13, 9, 28, 29, 15, 31, 8, 33, 17, 35, 36, 37, 19, 39, 10, 41, 21, 43, 22, 45, 23, 47, 48, 49, 25, 51, 52, 53, 9, 55, 28, 19, 29, 59, 6, 61, 31, 63, 64, 13, 33, 67, 17, 69, 35, 71, 12, 73, 37, 75, 76, 77, 39, 79, 40, 81, 41, 83, 84]

cp's OEIS Frontend

A349164 a(n) = A064989(A003961(n) / 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	1
3	3
4	4
5	5
6	3
7	7
8	4
9	9
10	5
11	11
12	12
13	13
14	7
15	15
16	16
17	17
18	9
19	19
20	2
21	21
22	11
23	23
24	4
25	25
26	13
27	9
28	28
29	29
30	15
31	31
32	8
33	33
34	17
35	35
36	36
37	37
38	19
39	39
40	10
41	41
42	21
43	43
44	22
45	45
46	23
47	47
48	48
49	49
50	25
51	51
52	52
53	53
54	9
55	55
56	28
57	19
58	29
59	59
60	6
61	61
62	31
63	63
64	64
65	13
66	33
67	67
68	17
69	69
70	35
71	71
72	12
73	73
74	37
75	75
76	76
77	77
78	39
79	79
80	40
81	81
82	41
83	83
84	84

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

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