A320536 - cp's OEIS frontend

A320536 a(n) is the least cardinal of a partition of {1..n} into simple paths of its divisorial graph.

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

[1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 10, 9, 10, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 11, 12, 12, 12, 12, 13, 12, 13, 13, 13, 13, 14, 14, 15, 15, 14, 14, 15, 14, 15, 15, 15, 15, 16, 16]

cp's OEIS Frontend

A320536 a(n) is the least cardinal of a partition of {1..n} into simple paths of its divisorial graph.

Table of values

List of values

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

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

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