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}$

This sequence is A001481 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-5}$ The Use of Computers in Number Theory: Exercise $3$