A327666 - cp's OEIS frontend

A327666 a(n) = Sum_{k = 1..n} (-1)^(Omega(k) - omega(k)), where Omega(k) counts prime factors of k with multiplicity and omega(k) counts distinct prime factors.

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

[1, 2, 3, 2, 3, 4, 5, 6, 5, 6, 7, 6, 7, 8, 9, 8, 9, 8, 9, 8, 9, 10, 11, 12, 11, 12, 13, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 26, 25, 26, 27, 26, 25, 24, 25, 24, 25, 26, 27, 28, 29, 30, 31, 30, 31, 32, 31, 30, 31, 32, 33, 32, 33, 34]

cp's OEIS Frontend

A327666 a(n) = Sum_{k = 1..n} (-1)^(Omega(k) - omega(k)), where Omega(k) counts prime factors of k with multiplicity and omega(k) counts distinct prime factors.

Table of values

List of values

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

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

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