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A349445 Dirichlet convolution of A001511 (the 2-adic valuation of 2n) with A349134 (the Dirichlet inverse of Kimberling's paraphrases).

Table of values

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

List of values

[1, 1, -1, 1, -2, -1, -3, 1, -2, -2, -5, -1, -6, -3, 0, 1, -8, -2, -9, -2, 0, -5, -11, -1, -6, -6, -4, -3, -14, 0, -15, 1, 0, -8, 0, -2, -18, -9, 0, -2, -20, 0, -21, -5, 2, -11, -23, -1, -12, -6, 0, -6, -26, -4, 0, -3, 0, -14, -29, 0, -30, -15, 3, 1, 0, 0, -33, -8, 0, 0, -35, -2, -36, -18, 4, -9, 0, 0, -39, -2, -8]