Table of Squares and Sums of Two Squares

== Table ==
The following table presents a list of all square numbers and numbers which can be expressed as the sum of $2$ squares up to $1000$.
In the following, $\map s n$ denotes the $n$th numbers which can be expressed as the sum of $2$ squares one of which may be $0$.
:$\begin{array} {|r|r|}
n & \map s n \\
\hline
1 & 0 \\
2 & 1 \\
3 & 2 \\
4 & 4 \\
5 & 5 \\
6 & 8 \\
7 & 9 \\
8 & 10 \\
9 & 13 \\
10 & 16 \\
11 & 17 \\
12 & 18 \\
13 & 20 \\
14 & 25 \\
15 & 26 \\
16 & 29 \\
17 & 32 \\
18 & 34 \\
19 & 36 \\
20 & 37 \\
21 & 40 \\
22 & 41 \\
23 & 45 \\
24 & 49 \\
25 & 50 \\
26 & 52 \\
27 & 53 \\
28 & 58 \\
29 & 61 \\
30 & 64 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
31 & 65 \\
32 & 68 \\
33 & 72 \\
34 & 73 \\
35 & 74 \\
36 & 80 \\
37 & 81 \\
38 & 82 \\
39 & 85 \\
40 & 89 \\
41 & 90 \\
42 & 97 \\
43 & 98 \\
44 & 100 \\
45 & 101 \\
46 & 104 \\
47 & 106 \\
48 & 109 \\
49 & 113 \\
50 & 116 \\
51 & 117 \\
52 & 121 \\
53 & 122 \\
54 & 125 \\
55 & 128 \\
56 & 130 \\
57 & 136 \\
58 & 137 \\
59 & 144 \\
60 & 145 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
61 & 146 \\
62 & 148 \\
63 & 149 \\
64 & 153 \\
65 & 157 \\
66 & 160 \\
67 & 162 \\
68 & 164 \\
69 & 169 \\
70 & 170 \\
71 & 173 \\
72 & 178 \\
73 & 180 \\
74 & 181 \\
75 & 185 \\
76 & 193 \\
77 & 194 \\
78 & 196 \\
79 & 197 \\
80 & 200 \\
81 & 202 \\
82 & 205 \\
83 & 208 \\
84 & 212 \\
85 & 218 \\
86 & 221 \\
87 & 225 \\
88 & 226 \\
89 & 229 \\
90 & 232 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
91 & 233 \\
92 & 234 \\
93 & 241 \\
94 & 242 \\
95 & 244 \\
96 & 245 \\
97 & 250 \\
98 & 256 \\
99 & 257 \\
100 & 260 \\
101 & 261 \\
102 & 265 \\
103 & 269 \\
104 & 272 \\
105 & 274 \\
106 & 277 \\
107 & 281 \\
108 & 288 \\
109 & 289 \\
110 & 290 \\
111 & 292 \\
112 & 293 \\
113 & 296 \\
114 & 298 \\
115 & 305 \\
116 & 306 \\
117 & 313 \\
118 & 314 \\
119 & 317 \\
120 & 320 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
121 & 324 \\
122 & 325 \\
123 & 328 \\
124 & 333 \\
125 & 337 \\
126 & 338 \\
127 & 340 \\
128 & 346 \\
129 & 349 \\
130 & 353 \\
131 & 356 \\
132 & 360 \\
133 & 361 \\
134 & 362 \\
135 & 365 \\
136 & 369 \\
137 & 370 \\
138 & 373 \\
139 & 377 \\
140 & 386 \\
141 & 388 \\
142 & 389 \\
143 & 392 \\
144 & 394 \\
145 & 397 \\
146 & 400 \\
147 & 401 \\
148 & 404 \\
149 & 405 \\
150 & 409 \\
\end{array}$
:$\begin{array} {|r|r|}
n & \map s n \\
\hline
151 & 410 \\
152 & 416 \\
153 & 421 \\
154 & 424 \\
155 & 425 \\
156 & 433 \\
157 & 436 \\
158 & 441 \\
159 & 442 \\
160 & 445 \\
161 & 449 \\
162 & 450 \\
163 & 452 \\
164 & 457 \\
165 & 458 \\
166 & 461 \\
167 & 464 \\
168 & 466 \\
169 & 468 \\
170 & 477 \\
171 & 481 \\
172 & 482 \\
173 & 484 \\
174 & 485 \\
175 & 488 \\
176 & 490 \\
177 & 493 \\
178 & 500 \\
179 & 505 \\
180 & 509 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
181 & 512 \\
182 & 514 \\
183 & 520 \\
184 & 521 \\
185 & 522 \\
186 & 529 \\
187 & 530 \\
188 & 533 \\
189 & 538 \\
190 & 541 \\
191 & 544 \\
192 & 545 \\
193 & 548 \\
194 & 549 \\
195 & 554 \\
196 & 557 \\
197 & 562 \\
198 & 565 \\
199 & 569 \\
200 & 576 \\
201 & 577 \\
202 & 578 \\
203 & 580 \\
204 & 584 \\
205 & 585 \\
206 & 586 \\
207 & 592 \\
208 & 593 \\
209 & 596 \\
210 & 601 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
211 & 605 \\
212 & 610 \\
213 & 612 \\
214 & 613 \\
215 & 617 \\
216 & 625 \\
217 & 626 \\
218 & 628 \\
219 & 629 \\
220 & 634 \\
221 & 637 \\
222 & 640 \\
223 & 641 \\
224 & 648 \\
225 & 650 \\
226 & 653 \\
227 & 656 \\
228 & 657 \\
229 & 661 \\
230 & 666 \\
231 & 673 \\
232 & 674 \\
233 & 676 \\
234 & 677 \\
235 & 680 \\
236 & 685 \\
237 & 689 \\
238 & 692 \\
239 & 697 \\
240 & 698 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
241 & 701 \\
242 & 706 \\
243 & 709 \\
244 & 712 \\
245 & 720 \\
246 & 722 \\
247 & 724 \\
248 & 725 \\
249 & 729 \\
250 & 730 \\
251 & 733 \\
252 & 738 \\
253 & 740 \\
254 & 745 \\
255 & 746 \\
256 & 754 \\
257 & 757 \\
258 & 761 \\
259 & 765 \\
260 & 769 \\
261 & 772 \\
262 & 773 \\
263 & 776 \\
264 & 778 \\
265 & 784 \\
266 & 785 \\
267 & 788 \\
268 & 793 \\
269 & 794 \\
270 & 797 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
271 & 800 \\
272 & 801 \\
273 & 802 \\
274 & 808 \\
275 & 809 \\
276 & 810 \\
277 & 818 \\
278 & 820 \\
279 & 821 \\
280 & 829 \\
281 & 832 \\
282 & 833 \\
283 & 841 \\
284 & 842 \\
285 & 845 \\
286 & 848 \\
287 & 850 \\
288 & 853 \\
289 & 857 \\
290 & 865 \\
291 & 866 \\
292 & 872 \\
293 & 873 \\
294 & 877 \\
295 & 881 \\
296 & 882 \\
297 & 884 \\
298 & 890 \\
299 & 898 \\
300 & 900 \\
\end{array} \qquad
\begin{array} {|r|r|}
n & \map s n \\
\hline
301 & 901 \\
302 & 904 \\
303 & 905 \\
304 & 909 \\
305 & 914 \\
306 & 916 \\
307 & 922 \\
308 & 925 \\
309 & 928 \\
310 & 929 \\
311 & 932 \\
312 & 936 \\
313 & 937 \\
314 & 941 \\
315 & 949 \\
316 & 953 \\
317 & 954 \\
318 & 961 \\
319 & 962 \\
320 & 964 \\
321 & 965 \\
322 & 968 \\
323 & 970 \\
324 & 976 \\
325 & 977 \\
326 & 980 \\
327 & 981 \\
328 & 985 \\
329 & 986 \\
330 & 997 \\
\end{array}$
== Sources ==
* : $\text {3-5}$ The Use of Computers in Number Theory: Exercise $3$
Category:Square Numbers
Category:Sums of Squares