A040004 - cp's OEIS frontend

A040004 a(n) = smallest integer s such that for all i, all primes p and all m the congruence (x_1)^n + ... + (x_s)^n == m (mod p^i) has a primitive solution.

n	a(n)
1	1
2	4
3	4
4	16
5	5
6	9
7	4
8	32
9	13
10	12
11	11
12	16
13	6
14	14
15	15
16	64
17	6
18	27
19	4
20	25
21	24
22	23
23	23
24	32
25	10
26	26
27	40
28	29
29	29
30	31
31	5
32	128
33	33
34	10
35	35
36	37
37	9
38	9
39	39
40	41
41	41
42	49
43	12
44	44
45	15
46	47
47	10
48	64
49	13
50	62
51	51
52	53
53	53
54	81
55	60
56	56
57	14
58	59
59	5
60	61
61	11
62	12
63	63
64	256
65	65
66	67
67	12
68	68
69	69

[1, 4, 4, 16, 5, 9, 4, 32, 13, 12, 11, 16, 6, 14, 15, 64, 6, 27, 4, 25, 24, 23, 23, 32, 10, 26, 40, 29, 29, 31, 5, 128, 33, 10, 35, 37, 9, 9, 39, 41, 41, 49, 12, 44, 15, 47, 10, 64, 13, 62, 51, 53, 53, 81, 60, 56, 14, 59, 5, 61, 11, 12, 63, 256, 65, 67, 12, 68, 69]

cp's OEIS Frontend

A040004 a(n) = smallest integer s such that for all i, all primes p and all m the congruence (x_1)^n + ... + (x_s)^n == m (mod p^i) has a primitive solution.

Table of values

List of values

n	a(n)
1	1
2	4
3	4
4	16
5	5
6	9
7	4
8	32
9	13
10	12
11	11
12	16
13	6
14	14
15	15
16	64
17	6
18	27
19	4
20	25
21	24
22	23
23	23
24	32
25	10
26	26
27	40
28	29
29	29
30	31
31	5
32	128
33	33
34	10
35	35
36	37
37	9
38	9
39	39
40	41
41	41
42	49
43	12
44	44
45	15
46	47
47	10
48	64
49	13
50	62
51	51
52	53
53	53
54	81
55	60
56	56
57	14
58	59
59	5
60	61
61	11
62	12
63	63
64	256
65	65
66	67
67	12
68	68
69	69

n	a(n)
1	1
2	4
3	4
4	16
5	5
6	9
7	4
8	32
9	13
10	12
11	11
12	16
13	6
14	14
15	15
16	64
17	6
18	27
19	4
20	25
21	24
22	23
23	23
24	32
25	10
26	26
27	40
28	29
29	29
30	31
31	5
32	128
33	33
34	10
35	35
36	37
37	9
38	9
39	39
40	41
41	41
42	49
43	12
44	44
45	15
46	47
47	10
48	64
49	13
50	62
51	51
52	53
53	53
54	81
55	60
56	56
57	14
58	59
59	5
60	61
61	11
62	12
63	63
64	256
65	65
66	67
67	12
68	68
69	69

n	a(n)
1	1
2	4
3	4
4	16
5	5
6	9
7	4
8	32
9	13
10	12
11	11
12	16
13	6
14	14
15	15
16	64
17	6
18	27
19	4
20	25
21	24
22	23
23	23
24	32
25	10
26	26
27	40
28	29
29	29
30	31
31	5
32	128
33	33
34	10
35	35
36	37
37	9
38	9
39	39
40	41
41	41
42	49
43	12
44	44
45	15
46	47
47	10
48	64
49	13
50	62
51	51
52	53
53	53
54	81
55	60
56	56
57	14
58	59
59	5
60	61
61	11
62	12
63	63
64	256
65	65
66	67
67	12
68	68
69	69