A341894 - cp's OEIS frontend

A341894 For square n > 0, a(n) = 0; for nonsquare n > 0, a(n) is the rank r such that t(r) + t(r-1) = u(r) - u(r-1) - 1, where u(r) and t(r) are indices of some triangular numbers in the Diophantine relation T(u(r)) = n*T(t(r)).

n	a(n)
1	0
2	1
3	1
4	0
5	2
6	2
7	2
8	2
9	0
10	3
11	2
12	2
13	4
14	2
15	2
16	0
17	2
18	2
19	3
20	2
21	4
22	4
23	2
24	2
25	0
26	3
27	2
28	4
29	4
30	2
31	4
32	2
33	2
34	2
35	2
36	0
37	2
38	2
39	2
40	4
41	4
42	2
43	4
44	2
45	4
46	6
47	2
48	2
49	0
50	3
51	3
52	4
53	4
54	2
55	4
56	2
57	4
58	4
59	2
60	2
61	8
62	2
63	2
64	0
65	2
66	4
67	4
68	2
69	4
70	4
71	4
72	2
73	6
74	2
75	2
76	6
77	4
78	4
79	2
80	2
81	0
82	3
83	2
84	2
85	8
86	4
87	2
88	4
89	4
90	2
91	6
92	4
93	4
94	4
95	2
96	4
97	4
98	2
99	2
100	0
101	2
102	2
103	4
104	2
105	4
106	8
107	2
108	2
109	8
110	2

[0, 1, 1, 0, 2, 2, 2, 2, 0, 3, 2, 2, 4, 2, 2, 0, 2, 2, 3, 2, 4, 4, 2, 2, 0, 3, 2, 4, 4, 2, 4, 2, 2, 2, 2, 0, 2, 2, 2, 4, 4, 2, 4, 2, 4, 6, 2, 2, 0, 3, 3, 4, 4, 2, 4, 2, 4, 4, 2, 2, 8, 2, 2, 0, 2, 4, 4, 2, 4, 4, 4, 2, 6, 2, 2, 6, 4, 4, 2, 2, 0, 3, 2, 2, 8, 4, 2, 4, 4, 2, 6, 4, 4, 4, 2, 4, 4, 2, 2, 0, 2, 2, 4, 2, 4, 8, 2, 2, 8, 2]

cp's OEIS Frontend

A341894 For square n > 0, a(n) = 0; for nonsquare n > 0, a(n) is the rank r such that t(r) + t(r-1) = u(r) - u(r-1) - 1, where u(r) and t(r) are indices of some triangular numbers in the Diophantine relation T(u(r)) = n*T(t(r)).

Table of values

List of values

n	a(n)
1	0
2	1
3	1
4	0
5	2
6	2
7	2
8	2
9	0
10	3
11	2
12	2
13	4
14	2
15	2
16	0
17	2
18	2
19	3
20	2
21	4
22	4
23	2
24	2
25	0
26	3
27	2
28	4
29	4
30	2
31	4
32	2
33	2
34	2
35	2
36	0
37	2
38	2
39	2
40	4
41	4
42	2
43	4
44	2
45	4
46	6
47	2
48	2
49	0
50	3
51	3
52	4
53	4
54	2
55	4
56	2
57	4
58	4
59	2
60	2
61	8
62	2
63	2
64	0
65	2
66	4
67	4
68	2
69	4
70	4
71	4
72	2
73	6
74	2
75	2
76	6
77	4
78	4
79	2
80	2
81	0
82	3
83	2
84	2
85	8
86	4
87	2
88	4
89	4
90	2
91	6
92	4
93	4
94	4
95	2
96	4
97	4
98	2
99	2
100	0
101	2
102	2
103	4
104	2
105	4
106	8
107	2
108	2
109	8
110	2

n	a(n)
1	0
2	1
3	1
4	0
5	2
6	2
7	2
8	2
9	0
10	3
11	2
12	2
13	4
14	2
15	2
16	0
17	2
18	2
19	3
20	2
21	4
22	4
23	2
24	2
25	0
26	3
27	2
28	4
29	4
30	2
31	4
32	2
33	2
34	2
35	2
36	0
37	2
38	2
39	2
40	4
41	4
42	2
43	4
44	2
45	4
46	6
47	2
48	2
49	0
50	3
51	3
52	4
53	4
54	2
55	4
56	2
57	4
58	4
59	2
60	2
61	8
62	2
63	2
64	0
65	2
66	4
67	4
68	2
69	4
70	4
71	4
72	2
73	6
74	2
75	2
76	6
77	4
78	4
79	2
80	2
81	0
82	3
83	2
84	2
85	8
86	4
87	2
88	4
89	4
90	2
91	6
92	4
93	4
94	4
95	2
96	4
97	4
98	2
99	2
100	0
101	2
102	2
103	4
104	2
105	4
106	8
107	2
108	2
109	8
110	2

n	a(n)
1	0
2	1
3	1
4	0
5	2
6	2
7	2
8	2
9	0
10	3
11	2
12	2
13	4
14	2
15	2
16	0
17	2
18	2
19	3
20	2
21	4
22	4
23	2
24	2
25	0
26	3
27	2
28	4
29	4
30	2
31	4
32	2
33	2
34	2
35	2
36	0
37	2
38	2
39	2
40	4
41	4
42	2
43	4
44	2
45	4
46	6
47	2
48	2
49	0
50	3
51	3
52	4
53	4
54	2
55	4
56	2
57	4
58	4
59	2
60	2
61	8
62	2
63	2
64	0
65	2
66	4
67	4
68	2
69	4
70	4
71	4
72	2
73	6
74	2
75	2
76	6
77	4
78	4
79	2
80	2
81	0
82	3
83	2
84	2
85	8
86	4
87	2
88	4
89	4
90	2
91	6
92	4
93	4
94	4
95	2
96	4
97	4
98	2
99	2
100	0
101	2
102	2
103	4
104	2
105	4
106	8
107	2
108	2
109	8
110	2