[seqfan] A072942

[Don Reble]

Seqfans:

    I emailed Phil: he agrees, A072942(18) is wrong. My values are below.

> %N Smallest number x such that x^n-1 factors only into its algebraic
>    factors.
> %C An exactly equivalent formulation is that a(n) is the least x such
>    that the cyclotomic polynomial values Phi(d,x) are prime for all d
>    dividing n.

    Perhaps the Exactly Equivalent Formulation should be the definition.
    That's why "2" never appears in the sequence: Phi(1,2) = 1, which
    is irreducible, but not prime.


 1 3
 2 4
 3 3
 4 4
 5 12
 6 6
 7 3
 8 4
 9 3
10 12
11 20
12 24687390
13 3
14 72
15 62
16 4
17 20
18 1102903830
19 12
20 58051620
21 3
22 1793172
23 468
24 1035844571580
25 62
26 882
27 398
28 75274140
29 6
30 81206805256038
31 14
32 1288005000
33 78428
34 93888
35 37664
36 24380304369772260
37 432
38 3300
39 21962
40 16066737508140
41 14
42 143657627809878
43 114
44 36352614120
45 22874682
46 8953500
47 62
48 ?
49 20550
50 3763118238
51 19388
52 37509098520
53 24
54 235734798214188
55 545948
56 257943509313180
57 101022
58 1335288
59 102
60 ?
61 138
62 25170
63 3
64 4109355036960
65 906902
66 ?
67 314
68 713139420
69 2278730
70 2355476281187040
71 3
72 ?
73 114
74 717528
75 1176582692
76 1791027390
77 204378
78 ?
79 140
80 ?
81 5960484
82 7154268
83 930
84 ?
85 199812
86 129918
87 3122672
88 ?
89 114
90 ?
91 208458
92 1125700552260
93 8664
94 145932
95 18618
96 ?
97 12
98 1410193452
99 401248874

-- 
Don Reble  djr at nk.ca


-- 
This message has been scanned for viruses and
dangerous content by MailScanner, and is
believed to be clean.