A089576 - cp's OEIS frontend

A089576 Let p_k = k-th prime, let f((p_k)^n) = m where m is the largest power of p_(k+1) < (p_k)^n. a(n) = number of iterations of f to reach 1, starting from n and starting from k = 1.

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

[0, 1, 2, 2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 21, 21]

cp's OEIS Frontend

A089576 Let p_k = k-th prime, let f((p_k)^n) = m where m is the largest power of p_(k+1) < (p_k)^n. a(n) = number of iterations of f to reach 1, starting from n and starting from k = 1.

Table of values

List of values

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

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

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