A256750 - cp's OEIS frontend

A256750 Start with n, and repeatedly apply the arithmetic derivative A003415. |a(n)| = the number of iterations to reach 0 (then a(n) is taken nonnegative) or a number having a factor of the form p^p with prime p, in which case a(n) = -|a(n)|.

n	a(n)
0	0
1	1
2	2
3	2
4	0
5	2
6	3
7	2
8	0
9	4
10	3
11	2
12	0
13	2
14	5
15	-1
16	0
17	2
18	5
19	2
20	0
21	4
22	3
23	2
24	0
25	4
26	-2
27	0
28	0
29	2
30	3
31	2
32	0
33	6
34	3
35	-1
36	0
37	2
38	5
39	-1
40	0
41	2
42	3
43	2
44	0
45	-2
46	5
47	2
48	0
49	6
50	-3
51	-1
52	0
53	2
54	0
55	-1
56	0
57	4
58	3
59	2
60	0
61	2
62	7
63	-2
64	0
65	6
66	3
67	2
68	0
69	-3
70	3
71	2
72	0
73	2
74	-2
75	-2
76	0
77	6
78	3
79	2
80	0
81	0
82	3
83	2
84	0
85	4
86	-3
87	-1
88	0
89	2
90	-2
91	-1
92	0
93	4
94	7
95	-1
96	0
97	2
98	7
99	-3

[0, 1, 2, 2, 0, 2, 3, 2, 0, 4, 3, 2, 0, 2, 5, -1, 0, 2, 5, 2, 0, 4, 3, 2, 0, 4, -2, 0, 0, 2, 3, 2, 0, 6, 3, -1, 0, 2, 5, -1, 0, 2, 3, 2, 0, -2, 5, 2, 0, 6, -3, -1, 0, 2, 0, -1, 0, 4, 3, 2, 0, 2, 7, -2, 0, 6, 3, 2, 0, -3, 3, 2, 0, 2, -2, -2, 0, 6, 3, 2, 0, 0, 3, 2, 0, 4, -3, -1, 0, 2, -2, -1, 0, 4, 7, -1, 0, 2, 7, -3]

cp's OEIS Frontend

A256750 Start with n, and repeatedly apply the arithmetic derivative A003415. |a(n)| = the number of iterations to reach 0 (then a(n) is taken nonnegative) or a number having a factor of the form p^p with prime p, in which case a(n) = -|a(n)|.

Table of values

List of values

n	a(n)
0	0
1	1
2	2
3	2
4	0
5	2
6	3
7	2
8	0
9	4
10	3
11	2
12	0
13	2
14	5
15	-1
16	0
17	2
18	5
19	2
20	0
21	4
22	3
23	2
24	0
25	4
26	-2
27	0
28	0
29	2
30	3
31	2
32	0
33	6
34	3
35	-1
36	0
37	2
38	5
39	-1
40	0
41	2
42	3
43	2
44	0
45	-2
46	5
47	2
48	0
49	6
50	-3
51	-1
52	0
53	2
54	0
55	-1
56	0
57	4
58	3
59	2
60	0
61	2
62	7
63	-2
64	0
65	6
66	3
67	2
68	0
69	-3
70	3
71	2
72	0
73	2
74	-2
75	-2
76	0
77	6
78	3
79	2
80	0
81	0
82	3
83	2
84	0
85	4
86	-3
87	-1
88	0
89	2
90	-2
91	-1
92	0
93	4
94	7
95	-1
96	0
97	2
98	7
99	-3

n	a(n)
0	0
1	1
2	2
3	2
4	0
5	2
6	3
7	2
8	0
9	4
10	3
11	2
12	0
13	2
14	5
15	-1
16	0
17	2
18	5
19	2
20	0
21	4
22	3
23	2
24	0
25	4
26	-2
27	0
28	0
29	2
30	3
31	2
32	0
33	6
34	3
35	-1
36	0
37	2
38	5
39	-1
40	0
41	2
42	3
43	2
44	0
45	-2
46	5
47	2
48	0
49	6
50	-3
51	-1
52	0
53	2
54	0
55	-1
56	0
57	4
58	3
59	2
60	0
61	2
62	7
63	-2
64	0
65	6
66	3
67	2
68	0
69	-3
70	3
71	2
72	0
73	2
74	-2
75	-2
76	0
77	6
78	3
79	2
80	0
81	0
82	3
83	2
84	0
85	4
86	-3
87	-1
88	0
89	2
90	-2
91	-1
92	0
93	4
94	7
95	-1
96	0
97	2
98	7
99	-3

n	a(n)
0	0
1	1
2	2
3	2
4	0
5	2
6	3
7	2
8	0
9	4
10	3
11	2
12	0
13	2
14	5
15	-1
16	0
17	2
18	5
19	2
20	0
21	4
22	3
23	2
24	0
25	4
26	-2
27	0
28	0
29	2
30	3
31	2
32	0
33	6
34	3
35	-1
36	0
37	2
38	5
39	-1
40	0
41	2
42	3
43	2
44	0
45	-2
46	5
47	2
48	0
49	6
50	-3
51	-1
52	0
53	2
54	0
55	-1
56	0
57	4
58	3
59	2
60	0
61	2
62	7
63	-2
64	0
65	6
66	3
67	2
68	0
69	-3
70	3
71	2
72	0
73	2
74	-2
75	-2
76	0
77	6
78	3
79	2
80	0
81	0
82	3
83	2
84	0
85	4
86	-3
87	-1
88	0
89	2
90	-2
91	-1
92	0
93	4
94	7
95	-1
96	0
97	2
98	7
99	-3