A263849 - cp's OEIS frontend

A263849 Let R = Z[(1+sqrt(5))/2] denote the ring of integers in the real quadratic number field of discriminant 5. Then a(n) is the largest integer k such that every totally positive element nu in R of norm m = A031363(n) can be written as a sum of three squares in R in at least k ways.

n	a(n)
0	1
1	6
2	12
3	24
4	32
5	24
6	54
7	24
8	24
9	30
10	24
11	48
12	48
13	96
14	24
15	48
16	96
17	48
18	24
19	120
20	108
21	48
22	72
23	48
24	120
25	54
26	48
27	48
28	48
29	84
30	72
31	120
32	72
33	78
34	48
35	144
36	72
37	72
38	128
39	192
40	120
41	96
42	48
43	48
44	96
45	96
46	216
47	72
48	48
49	120
50	96
51	96
52	48
53	96
54	48
55	120
56	96
57	224
58	72
59	120
60	48
61	288
62	72
63	48
64	72
65	246
66	240
67	120
68	144

[1, 6, 12, 24, 32, 24, 54, 24, 24, 30, 24, 48, 48, 96, 24, 48, 96, 48, 24, 120, 108, 48, 72, 48, 120, 54, 48, 48, 48, 84, 72, 120, 72, 78, 48, 144, 72, 72, 128, 192, 120, 96, 48, 48, 96, 96, 216, 72, 48, 120, 96, 96, 48, 96, 48, 120, 96, 224, 72, 120, 48, 288, 72, 48, 72, 246, 240, 120, 144]

cp's OEIS Frontend

A263849 Let R = Z[(1+sqrt(5))/2] denote the ring of integers in the real quadratic number field of discriminant 5. Then a(n) is the largest integer k such that every totally positive element nu in R of norm m = A031363(n) can be written as a sum of three squares in R in at least k ways.

Table of values

List of values

n	a(n)
0	1
1	6
2	12
3	24
4	32
5	24
6	54
7	24
8	24
9	30
10	24
11	48
12	48
13	96
14	24
15	48
16	96
17	48
18	24
19	120
20	108
21	48
22	72
23	48
24	120
25	54
26	48
27	48
28	48
29	84
30	72
31	120
32	72
33	78
34	48
35	144
36	72
37	72
38	128
39	192
40	120
41	96
42	48
43	48
44	96
45	96
46	216
47	72
48	48
49	120
50	96
51	96
52	48
53	96
54	48
55	120
56	96
57	224
58	72
59	120
60	48
61	288
62	72
63	48
64	72
65	246
66	240
67	120
68	144

n	a(n)
0	1
1	6
2	12
3	24
4	32
5	24
6	54
7	24
8	24
9	30
10	24
11	48
12	48
13	96
14	24
15	48
16	96
17	48
18	24
19	120
20	108
21	48
22	72
23	48
24	120
25	54
26	48
27	48
28	48
29	84
30	72
31	120
32	72
33	78
34	48
35	144
36	72
37	72
38	128
39	192
40	120
41	96
42	48
43	48
44	96
45	96
46	216
47	72
48	48
49	120
50	96
51	96
52	48
53	96
54	48
55	120
56	96
57	224
58	72
59	120
60	48
61	288
62	72
63	48
64	72
65	246
66	240
67	120
68	144

n	a(n)
0	1
1	6
2	12
3	24
4	32
5	24
6	54
7	24
8	24
9	30
10	24
11	48
12	48
13	96
14	24
15	48
16	96
17	48
18	24
19	120
20	108
21	48
22	72
23	48
24	120
25	54
26	48
27	48
28	48
29	84
30	72
31	120
32	72
33	78
34	48
35	144
36	72
37	72
38	128
39	192
40	120
41	96
42	48
43	48
44	96
45	96
46	216
47	72
48	48
49	120
50	96
51	96
52	48
53	96
54	48
55	120
56	96
57	224
58	72
59	120
60	48
61	288
62	72
63	48
64	72
65	246
66	240
67	120
68	144