A323355 - cp's OEIS frontend

A323355 a(1)=1; for n >= 2, a(n) = Sum_{i=1..A000120(n)} a(z(i)), where z(i) are the positions of 1's in the binary expansion of n, counted from left to right.

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

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

cp's OEIS Frontend

A323355 a(1)=1; for n >= 2, a(n) = Sum_{i=1..A000120(n)} a(z(i)), where z(i) are the positions of 1's in the binary expansion of n, counted from left to right.

Table of values

List of values

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

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

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