A258851 - cp's OEIS frontend

A258851 The pi-based arithmetic derivative of n: a(p) = pi(p) for p prime, a(uv) = a(u)v + u*a(v), where pi = A000720.

n	a(n)
0	0
1	0
2	1
3	2
4	4
5	3
6	7
7	4
8	12
9	12
10	11
11	5
12	20
13	6
14	15
15	19
16	32
17	7
18	33
19	8
20	32
21	26
22	21
23	9
24	52
25	30
26	25
27	54
28	44
29	10
30	53
31	11
32	80
33	37
34	31
35	41
36	84
37	12
38	35
39	44
40	84
41	13
42	73
43	14
44	64
45	87
46	41
47	15
48	128
49	56
50	85
51	55
52	76
53	16
54	135
55	58
56	116
57	62
58	49
59	17
60	136
61	18
62	53
63	120
64	192
65	69
66	107

[0, 0, 1, 2, 4, 3, 7, 4, 12, 12, 11, 5, 20, 6, 15, 19, 32, 7, 33, 8, 32, 26, 21, 9, 52, 30, 25, 54, 44, 10, 53, 11, 80, 37, 31, 41, 84, 12, 35, 44, 84, 13, 73, 14, 64, 87, 41, 15, 128, 56, 85, 55, 76, 16, 135, 58, 116, 62, 49, 17, 136, 18, 53, 120, 192, 69, 107]

cp's OEIS Frontend

A258851 The pi-based arithmetic derivative of n: a(p) = pi(p) for p prime, a(uv) = a(u)v + u*a(v), where pi = A000720.

Table of values

List of values

n	a(n)
0	0
1	0
2	1
3	2
4	4
5	3
6	7
7	4
8	12
9	12
10	11
11	5
12	20
13	6
14	15
15	19
16	32
17	7
18	33
19	8
20	32
21	26
22	21
23	9
24	52
25	30
26	25
27	54
28	44
29	10
30	53
31	11
32	80
33	37
34	31
35	41
36	84
37	12
38	35
39	44
40	84
41	13
42	73
43	14
44	64
45	87
46	41
47	15
48	128
49	56
50	85
51	55
52	76
53	16
54	135
55	58
56	116
57	62
58	49
59	17
60	136
61	18
62	53
63	120
64	192
65	69
66	107

n	a(n)
0	0
1	0
2	1
3	2
4	4
5	3
6	7
7	4
8	12
9	12
10	11
11	5
12	20
13	6
14	15
15	19
16	32
17	7
18	33
19	8
20	32
21	26
22	21
23	9
24	52
25	30
26	25
27	54
28	44
29	10
30	53
31	11
32	80
33	37
34	31
35	41
36	84
37	12
38	35
39	44
40	84
41	13
42	73
43	14
44	64
45	87
46	41
47	15
48	128
49	56
50	85
51	55
52	76
53	16
54	135
55	58
56	116
57	62
58	49
59	17
60	136
61	18
62	53
63	120
64	192
65	69
66	107

cp's OEIS Frontend

A258851 The pi-based arithmetic derivative of n: a(p) = pi(p) for p prime, a(u*v) = a(u)*v + u*a(v), where pi = A000720.

Table of values

List of values

A258851 The pi-based arithmetic derivative of n: a(p) = pi(p) for p prime, a(uv) = a(u)v + u*a(v), where pi = A000720.

n	a(n)
0	0
1	0
2	1
3	2
4	4
5	3
6	7
7	4
8	12
9	12
10	11
11	5
12	20
13	6
14	15
15	19
16	32
17	7
18	33
19	8
20	32
21	26
22	21
23	9
24	52
25	30
26	25
27	54
28	44
29	10
30	53
31	11
32	80
33	37
34	31
35	41
36	84
37	12
38	35
39	44
40	84
41	13
42	73
43	14
44	64
45	87
46	41
47	15
48	128
49	56
50	85
51	55
52	76
53	16
54	135
55	58
56	116
57	62
58	49
59	17
60	136
61	18
62	53
63	120
64	192
65	69
66	107