A329570 - cp's OEIS frontend

A329570 a(n) is the least prime P such that log(P)/log(p) >= valuation(n,p) for all primes p.

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

[2, 2, 3, 5, 5, 3, 7, 11, 11, 5, 11, 5, 13, 7, 5, 17, 17, 11, 19, 5, 7, 11, 23, 11, 29, 13, 29, 7, 29, 5, 31, 37, 11, 17, 7, 11, 37, 19, 13, 11, 41, 7, 43, 11, 11, 23, 47, 17, 53, 29, 17, 13, 53, 29, 11, 11, 19, 29, 59, 5, 61, 31, 11, 67, 13, 11, 67, 17, 23, 7, 71, 11, 73, 37, 29, 19, 11]

cp's OEIS Frontend

A329570 a(n) is the least prime P such that log(P)/log(p) >= valuation(n,p) for all primes p.

Table of values

List of values

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

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

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