A125142 - cp's OEIS frontend

A125142 a(n) = smallest k such that SEPSigma^{k}(n)=1, or -1 if no such k exists. Here SEPSigma(m) = (-1)^(Sum_i r_i)Sum_{d|m} (-1)^(Sum_j Max(r_j))d =Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^r_i where m=Product_i p_i^r_i, d=Product_j p_j^r_j, p_j^max(r_j) is the largest power of p_j dividing m.

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

[0, 1, 2, 4, 5, 2, 3, 6, 6, 5, 6, 4, 5, 3, 7, 9, 10, 6, 7, 7, 5, 6, 7, 6, 9, 5, 8, 6, 7, 7, 8, 11, 8, 10, 7, -1, -1, 7, 7, -1, -1, 5, 6, 8, -1, 7, 8, 9, -1, 9, 12, -1, -1, 8, -1, 8, -1, 7, 8, 9, 10, 8, 8, 10, 10, 8, 9, 12, 9, 7, 8, -1, -1, -1, 9, 9, 10, 7, 8, 12, -1, -1, -1, -1, 11, 6, 9, 11, 12, -1]

cp's OEIS Frontend

A125142 a(n) = smallest k such that SEPSigma^{k}(n)=1, or -1 if no such k exists. Here SEPSigma(m) = (-1)^(Sum_i r_i)Sum_{d|m} (-1)^(Sum_j Max(r_j))d =Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^r_i where m=Product_i p_i^r_i, d=Product_j p_j^r_j, p_j^max(r_j) is the largest power of p_j dividing m.

Table of values

List of values

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

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

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