[seqfan] A072995

Don Reble djr at nk.ca
Sun Feb 23 11:23:43 CET 2014


> %I A072995
> %N Least k such that the number of solutions to x^k==1 (mod k) 1<=x<=k
>    is equal to n.

> %C ... It thus appears that a(2^k)=2^(k+1), for k=1,2,3,.... Is this
>    known to be true? - John W. Layman (layman(AT)math.vt.edu)

    It's true. (One could have defined the sequence so that a(1)=2:
    then it would be true for 2^0 also. Too late now, I suppose.)

> %C a(30), if it exists, is greater than 400000.
>    - Ryan Propper (rpropper(AT)stanford.edu), Sep 10 2005

    a(30) doesn't exist. (If N is even, and divisible by D different odd
    primes, but not divisible by 2^D, then a(N) doesn't exist.)
    I propose "or 0 if there is no such k" in the definition.

    Have s'more terms.

%S A072995 1,4,9,8,25,18,49,16,27,50,121,36,169,98,225,32,289,54,361,110,147,
%T A072995 242,529,72,125,338,81,196,841,0,961,64,1089,578,1225,108,1369,722,
%U A072995 507,100,1681,0,1849,484,675,1058,2209,144,343,250,2601,1378,2809

1 1
2 4
3 9
4 8
5 25
6 18
7 49
8 16
9 27
10 50
11 121
12 36
13 169
14 98
15 225
16 32
17 289
18 54
19 361
20 110
21 147
22 242
23 529
24 72
25 125
26 338
27 81
28 196
29 841
30 0
31 961
32 64
33 1089
34 578
35 1225
36 108
37 1369
38 722
39 507
40 100
41 1681
42 0
43 1849
44 484
45 675
46 1058
47 2209
48 144
49 343
50 250
51 2601
52 1378
53 2809
54 162
55 605
56 392
57 1083
58 1682
59 3481
60 450
61 3721
62 1922
63 441
64 128
65 4225
66 0
67 4489
68 1734
69 4761
70 0
71 5041
72 216
73 5329
74 2738
75 1125
76 1444
77 5929
78 0
79 6241
80 200
81 243
82 3362
83 6889
84 294
85 7225
86 3698
87 7569
88 968
89 7921
90 0
91 8281
92 2116
93 2883
94 4418
95 9025
96 288
97 9409
98 686
99 3267
100 550
101 10201
102 0
103 10609
104 676
105 3675
106 5618
107 11449
108 324
109 11881
110 0
111 4107
112 784
113 12769
114 0
115 13225
116 3422
117 1521
118 6962
119 14161
120 930
121 1331
122 7442
123 15129
124 3844
125 625
126 0
127 16129
128 256
129 5547
130 0
131 17161
132 2178
133 17689
134 8978
135 2025
136 1156
137 18769
138 0
139 19321
140 2450
141 19881
142 10082
143 20449
144 432
145 21025
146 10658
147 1029
148 11026
149 22201
150 0
151 22801
152 2888
153 7803
154 0
155 4805
156 1014
157 24649
158 12482
159 25281
160 400
161 25921
162 486
163 26569
164 6806
165 5445
166 13778
167 27889
168 588
169 2197
170 0
171 7581
172 7396
173 29929
174 0
175 6125
176 1936
177 31329
178 15842
179 32041
180 1350
181 32761
182 0
183 11163
184 4232
185 34225
186 0
187 34969
188 8836
189 1323
190 0
191 36481
192 576
193 37249
194 18818
195 12675
196 1372
197 38809
198 0
199 39601
200 500

-- 
Don Reble  djr at nk.ca


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