A080361 - cp's OEIS frontend

A080361 a(n) is the difference between the largest and the smallest positive integers x such that the number of unitary-prime-divisors of x! equals n. Same as the difference between the largest and the smallest positive integers x such that the number of primes in (x/2,x] equals n.

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

[8, 13, 15, 21, 15, 15, 13, 9, 25, 27, 5, 23, 39, 37, 27, 21, 7, 45, 37, 39, 39, 1, 21, 17, 11, 35, 27, 53, 35, 17, 19, 27, 29, 9, 11, 11, 5, 21, 43, 27, 11, 69, 61, 63, 15, 5, 1, 5, 33, 29, 27, 5, 5, 17, 57, 43, 47, 17, 25, 51, 47, 11, 3, 25, 27, 23, 77, 57, 35, 19, 29, 37, 27, 23, 9]

cp's OEIS Frontend

A080361 a(n) is the difference between the largest and the smallest positive integers x such that the number of unitary-prime-divisors of x! equals n. Same as the difference between the largest and the smallest 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	8
2	13
3	15
4	21
5	15
6	15
7	13
8	9
9	25
10	27
11	5
12	23
13	39
14	37
15	27
16	21
17	7
18	45
19	37
20	39
21	39
22	1
23	21
24	17
25	11
26	35
27	27
28	53
29	35
30	17
31	19
32	27
33	29
34	9
35	11
36	11
37	5
38	21
39	43
40	27
41	11
42	69
43	61
44	63
45	15
46	5
47	1
48	5
49	33
50	29
51	27
52	5
53	5
54	17
55	57
56	43
57	47
58	17
59	25
60	51
61	47
62	11
63	3
64	25
65	27
66	23
67	77
68	57
69	35
70	19
71	29
72	37
73	27
74	23
75	9

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

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