A133948 - cp's OEIS frontend

A133948 a(n) = the number of "isolated divisors" of n(n+1). A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.

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

[0, 1, 2, 2, 3, 3, 4, 6, 5, 4, 6, 6, 4, 8, 12, 6, 7, 7, 6, 13, 9, 4, 10, 16, 8, 11, 16, 8, 9, 9, 8, 16, 11, 12, 21, 12, 4, 11, 22, 10, 9, 9, 8, 24, 15, 4, 14, 21, 14, 17, 16, 8, 11, 22, 22, 23, 11, 4, 16, 16, 4, 17, 32, 22, 23, 11, 8, 18, 22, 12, 16, 16, 4, 17, 26, 20, 21, 11, 14, 37, 15, 4, 16]

cp's OEIS Frontend

A133948 a(n) = the number of "isolated divisors" of n(n+1). A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.

Table of values

List of values

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

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

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