A080362 - cp's OEIS frontend

A080362 a(n) is the number of positive integers x such that the number of unitary-prime-divisors of x! equals n. Same as the number of positive integers x such that the number of primes in (x/2,x] equals n.

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

[4, 10, 7, 14, 7, 10, 12, 5, 14, 16, 3, 10, 18, 16, 15, 11, 7, 16, 19, 14, 9, 2, 14, 14, 8, 11, 18, 19, 24, 10, 14, 16, 20, 10, 11, 3, 6, 13, 18, 21, 9, 31, 37, 10, 15, 6, 2, 6, 21, 12, 7, 6, 6, 16, 15, 34, 14, 10, 15, 29, 22, 9, 4, 14, 16, 17, 25, 36, 12, 15, 13, 19, 19, 8, 10, 5, 12]

cp's OEIS Frontend

A080362 a(n) is the number of positive integers x such that the number of unitary-prime-divisors of x! equals n. Same as the number of positive integers x such that the number of primes in (x/2,x] equals n.

Table of values

List of values

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

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

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