Attractive Numbers, Perl

Attractive Numbers

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#perl 5.22.1

%isPrime=(2=>3,3=>5,5=>7,7=>11,11=>-1,largest=>11);
for (1..1000){
  primeFactors($_)
}

sub primeFactors{
   my $wn=$number=shift;
   my @factorsList=();
   my $test=2; $limit=sqrt($wn+1);
   while ($test < $limit){
     if  ($wn % $test){
         $test=$isPrime{$test};
     }
     else{
      push @factorsList,$test;
      storePrime($test);
      $wn=$wn/$test;
      $limit=sqrt($wn+1)      
     }
   }
   push @factorsList,$wn;
   if (scalar @factorsList == 1){
      print "$number is prime\n";
      storePrime($number);
   }
   else{
     print "$number   :factors are ", join ",",@factorsList,($isPrime{scalar @factorsList})? "and is attractive\n":"\n" 
     };
   
  sub storePrime{
    my $p=shift;
    if($p>$isPrime{largest}){
          @isPrime{$p,$isPrime{"largest"},"largest"}=(-1,$p,$p);
      }
  }
   
}

__DATA__
Stash in a Hash

Calling a function that yields a consistent result does provide an oprtunity for saving processing power.  One could remeber the reults, and bypass the computation altogether, retrieving the results from our store. In doing so one sacrifices space (for storing results) to achive better performance. But having a function that 1) checks if a there has been a prior call with the samae parameters, if so retrieve results of the operation,  OTHERWISE   2) store the results for future retrieval itself takes up processing time.  Thus the difference is not always noticeable for infrequently called functions.

a function that derives prime factors is one such processing task.
1) one could sequentially try test factors incrementally up to reasonable limit (sqrt(N)+1), dividing by factors (which will automatically be prime) discovered, and reducing the limit at each discovery of a factor.
2) One could store prime numbers discovered, in a hash and only test these incrementally.  Instead of incrementing the test factors, we could test the next available prime factor (stored in a hash).  If no prime factor, this could be stored in that hash of potential prime factors.
3) one could store prime numbers and previously discovered prime factors storing the results in an array

Lets try each of these and chart the results for varying sizes of inputs:-

Where it makes a significant difference is during large recursive procedures. The leornado function (and other similar functions like fibonnaci series can be such procedures).  These appear to require quadratically more

[ + ] Show input
Absolute running time: 0.08 sec, cpu time: 0.02 sec, memory peak: 3 Mb, absolute service time: 0,09 sec

1 is prime 2 is prime 3 is prime 4 :factors are 2,2,and is attractive 5 is prime 6 :factors are 2,3,and is attractive 7 is prime 8 :factors are 2,2,2,and is attractive 9 :factors are 3,3,and is attractive 10 :factors are 2,5,and is attractive 11 is prime 12 :factors are 2,2,3,and is attractive 13 is prime 14 :factors are 2,7,and is attractive 15 :factors are 3,5,and is attractive 16 :factors are 2,2,2,2, 17 is prime 18 :factors are 2,3,3,and is attractive 19 is prime 20 :factors are 2,2,5,and is attractive 21 :factors are 3,7,and is attractive 22 :factors are 2,11,and is attractive 23 is prime 24 :factors are 2,2,2,3, 25 :factors are 5,5,and is attractive 26 :factors are 2,13,and is attractive 27 :factors are 3,3,3,and is attractive 28 :factors are 2,2,7,and is attractive 29 is prime 30 :factors are 2,3,5,and is attractive 31 is prime 32 :factors are 2,2,2,2,2,and is attractive 33 :factors are 3,11,and is attractive 34 :factors are 2,17,and is attractive 35 :factors are 5,7,and is attractive 36 :factors are 2,2,3,3, 37 is prime 38 :factors are 2,19,and is attractive 39 :factors are 3,13,and is attractive 40 :factors are 2,2,2,5, 41 is prime 42 :factors are 2,3,7,and is attractive 43 is prime 44 :factors are 2,2,11,and is attractive 45 :factors are 3,3,5,and is attractive 46 :factors are 2,23,and is attractive 47 is prime 48 :factors are 2,2,2,2,3,and is attractive 49 :factors are 7,7,and is attractive 50 :factors are 2,5,5,and is attractive 51 :factors are 3,17,and is attractive 52 :factors are 2,2,13,and is attractive 53 is prime 54 :factors are 2,3,3,3, 55 :factors are 5,11,and is attractive 56 :factors are 2,2,2,7, 57 :factors are 3,19,and is attractive 58 :factors are 2,29,and is attractive 59 is prime 60 :factors are 2,2,3,5, 61 is prime 62 :factors are 2,31,and is attractive 63 :factors are 3,3,7,and is attractive 64 :factors are 2,2,2,2,2,2, 65 :factors are 5,13,and is attractive 66 :factors are 2,3,11,and is attractive 67 is prime 68 :factors are 2,2,17,and is attractive 69 :factors are 3,23,and is attractive 70 :factors are 2,5,7,and is attractive 71 is prime 72 :factors are 2,2,2,3,3,and is attractive 73 is prime 74 :factors are 2,37,and is attractive 75 :factors are 3,5,5,and is attractive 76 :factors are 2,2,19,and is attractive 77 :factors are 7,11,and is attractive 78 :factors are 2,3,13,and is attractive 79 is prime 80 :factors are 2,2,2,2,5,and is attractive 81 :factors are 3,3,3,3, 82 :factors are 2,41,and is attractive 83 is prime 84 :factors are 2,2,3,7, 85 :factors are 5,17,and is attractive 86 :factors are 2,43,and is attractive 87 :factors are 3,29,and is attractive 88 :factors are 2,2,2,11, 89 is prime 90 :factors are 2,3,3,5, 91 :factors are 7,13,and is attractive 92 :factors are 2,2,23,and is attractive 93 :factors are 3,31,and is attractive 94 :factors are 2,47,and is attractive 95 :factors are 5,19,and is attractive 96 :factors are 2,2,2,2,2,3, 97 is prime 98 :factors are 2,7,7,and is attractive 99 :factors are 3,3,11,and is attractive 100 :factors are 2,2,5,5, 101 is prime 102 :factors are 2,3,17,and is attractive 103 is prime 104 :factors are 2,2,2,13, 105 :factors are 3,5,7,and is attractive 106 :factors are 2,53,and is attractive 107 is prime 108 :factors are 2,2,3,3,3,and is attractive 109 is prime 110 :factors are 2,5,11,and is attractive 111 :factors are 3,37,and is attractive 112 :factors are 2,2,2,2,7,and is attractive 113 is prime 114 :factors are 2,3,19,and is attractive 115 :factors are 5,23,and is attractive 116 :factors are 2,2,29,and is attractive 117 :factors are 3,3,13,and is attractive 118 :factors are 2,59,and is attractive 119 :factors are 7,17,and is attractive 120 :factors are 2,2,2,3,5,and is attractive 121 :factors are 11,11,and is attractive 122 :factors are 2,61,and is attractive 123 :factors are 3,41,and is attractive 124 :factors are 2,2,31,and is attractive 125 :factors are 5,5,5,and is attractive 126 :factors are 2,3,3,7, 127 is prime 128 :factors are 2,2,2,2,2,2,2,and is attractive 129 :factors are 3,43,and is attractive 130 :factors are 2,5,13,and is attractive 131 is prime 132 :factors are 2,2,3,11, 133 :factors are 7,19,and is attractive 134 :factors are 2,67,and is attractive 135 :factors are 3,3,3,5, 136 :factors are 2,2,2,17, 137 is prime 138 :factors are 2,3,23,and is attractive 139 is prime 140 :factors are 2,2,5,7, 141 :factors are 3,47,and is attractive 142 :factors are 2,71,and is attractive 143 :factors are 11,13,and is attractive 144 :factors are 2,2,2,2,3,3, 145 :factors are 5,29,and is attractive 146 :factors are 2,73,and is attractive 147 :factors are 3,7,7,and is attractive 148 :factors are 2,2,37,and is attractive 149 is prime 150 :factors are 2,3,5,5, 151 is prime 152 :factors are 2,2,2,19, 153 :factors are 3,3,17,and is attractive 154 :factors are 2,7,11,and is attractive 155 :factors are 5,31,and is attractive 156 :factors are 2,2,3,13, 157 is prime 158 :factors are 2,79,and is attractive 159 :factors are 3,53,and is attractive 160 :factors are 2,2,2,2,2,5, 161 :factors are 7,23,and is attractive 162 :factors are 2,3,3,3,3,and is attractive 163 is prime 164 :factors are 2,2,41,and is attractive 165 :factors are 3,5,11,and is attractive 166 :factors are 2,83,and is attractive 167 is prime 168 :factors are 2,2,2,3,7,and is attractive 169 :factors are 13,13,and is attractive 170 :factors are 2,5,17,and is attractive 171 :factors are 3,3,19,and is attractive 172 :factors are 2,2,43,and is attractive 173 is prime 174 :factors are 2,3,29,and is attractive 175 :factors are 5,5,7,and is attractive 176 :factors are 2,2,2,2,11,and is attractive 177 :factors are 3,59,and is attractive 178 :factors are 2,89,and is attractive 179 is prime 180 :factors are 2,2,3,3,5,and is attractive 181 is prime 182 :factors are 2,7,13,and is attractive 183 :factors are 3,61,and is attractive 184 :factors are 2,2,2,23, 185 :factors are 5,37,and is attractive 186 :factors are 2,3,31,and is attractive 187 :factors are 11,17,and is attractive 188 :factors are 2,2,47,and is attractive 189 :factors are 3,3,3,7, 190 :factors are 2,5,19,and is attractive 191 is prime 192 :factors are 2,2,2,2,2,2,3,and is attractive 193 is prime 194 :factors are 2,97,and is attractive 195 :factors are 3,5,13,and is attractive 196 :factors are 2,2,7,7, 197 is prime 198 :factors are 2,3,3,11, 199 is prime 200 :factors are 2,2,2,5,5,and is attractive 201 :factors are 3,67,and is attractive 202 :factors are 2,101,and is attractive 203 :factors are 7,29,and is attractive 204 :factors are 2,2,3,17, 205 :factors are 5,41,and is attractive 206 :factors are 2,103,and is attractive 207 :factors are 3,3,23,and is attractive 208 :factors are 2,2,2,2,13,and is attractive 209 :factors are 11,19,and is attractive 210 :factors are 2,3,5,7, 211 is prime 212 :factors are 2,2,53,and is attractive 213 :factors are 3,71,and is attractive 214 :factors are 2,107,and is attractive 215 :factors are 5,43,and is attractive 216 :factors are 2,2,2,3,3,3, 217 :factors are 7,31,and is attractive 218 :factors are 2,109,and is attractive 219 :factors are 3,73,and is attractive 220 :factors are 2,2,5,11, 221 :factors are 13,17,and is attractive 222 :factors are 2,3,37,and is attractive 223 is prime 224 :factors are 2,2,2,2,2,7, 225 :factors are 3,3,5,5, 226 :factors are 2,113,and is attractive 227 is prime 228 :factors are 2,2,3,19, 229 is prime 230 :factors are 2,5,23,and is attractive 231 :factors are 3,7,11,and is attractive 232 :factors are 2,2,2,29, 233 is prime 234 :factors are 2,3,3,13, 235 :factors are 5,47,and is attractive 236 :factors are 2,2,59,and is attractive 237 :factors are 3,79,and is attractive 238 :factors are 2,7,17,and is attractive 239 is prime 240 :factors are 2,2,2,2,3,5, 241 is prime 242 :factors are 2,11,11,and is attractive 243 :factors are 3,3,3,3,3,and is attractive 244 :factors are 2,2,61,and is attractive 245 :factors are 5,7,7,and is attractive 246 :factors are 2,3,41,and is attractive 247 :factors are 13,19,and is attractive 248 :factors are 2,2,2,31, 249 :factors are 3,83,and is attractive 250 :factors are 2,5,5,5, 251 is prime 252 :factors are 2,2,3,3,7,and is attractive 253 :factors are 11,23,and is attractive 254 :factors are 2,127,and is attractive 255 :factors are 3,5,17,and is attractive 256 :factors are 2,2,2,2,2,2,2,2, 257 is prime 258 :factors are 2,3,43,and is attractive 259 :factors are 7,37,and is attractive 260 :factors are 2,2,5,13, 261 :factors are 3,3,29,and is attractive 262 :factors are 2,131,and is attractive 263 is prime 264 :factors are 2,2,2,3,11,and is attractive 265 :factors are 5,53,and is attractive 266 :factors are 2,7,19,and is attractive 267 :factors are 3,89,and is attractive 268 :factors are 2,2,67,and is attractive 269 is prime 270 :factors are 2,3,3,3,5,and is attractive 271 is prime 272 :factors are 2,2,2,2,17,and is attractive 273 :factors are 3,7,13,and is attractive 274 :factors are 2,137,and is attractive 275 :factors are 5,5,11,and is attractive 276 :factors are 2,2,3,23, 277 is prime 278 :factors are 2,139,and is attractive 279 :factors are 3,3,31,and is attractive 280 :factors are 2,2,2,5,7,and is attractive 281 is prime 282 :factors are 2,3,47,and is attractive 283 is prime 284 :factors are 2,2,71,and is attractive 285 :factors are 3,5,19,and is attractive 286 :factors are 2,11,13,and is attractive 287 :factors are 7,41,and is attractive 288 :factors are 2,2,2,2,2,3,3,and is attractive 289 :factors are 17,17,and is attractive 290 :factors are 2,5,29,and is attractive 291 :factors are 3,97,and is attractive 292 :factors are 2,2,73,and is attractive 293 is prime 294 :factors are 2,3,7,7, 295 :factors are 5,59,and is attractive 296 :factors are 2,2,2,37, 297 :factors are 3,3,3,11, 298 :factors are 2,149,and is attractive 299 :factors are 13,23,and is attractive 300 :factors are 2,2,3,5,5,and is attractive 301 :factors are 7,43,and is attractive 302 :factors are 2,151,and is attractive 303 :factors are 3,101,and is attractive 304 :factors are 2,2,2,2,19,and is attractive 305 :factors are 5,61,and is attractive 306 :factors are 2,3,3,17, 307 is prime 308 :factors are 2,2,7,11, 309 :factors are 3,103,and is attractive 310 :factors are 2,5,31,and is attractive 311 is prime 312 :factors are 2,2,2,3,13,and is attractive 313 is prime 314 :factors are 2,157,and is attractive 315 :factors are 3,3,5,7, 316 :factors are 2,2,79,and is attractive 317 is prime 318 :factors are 2,3,53,and is attractive 319 :factors are 11,29,and is attractive 320 :factors are 2,2,2,2,2,2,5,and is attractive 321 :factors are 3,107,and is attractive 322 :factors are 2,7,23,and is attractive 323 :factors are 17,19,and is attractive 324 :factors are 2,2,3,3,3,3, 325 :factors are 5,5,13,and is attractive 326 :factors are 2,163,and is attractive 327 :factors are 3,109,and is attractive 328 :factors are 2,2,2,41, 329 :factors are 7,47,and is attractive 330 :factors are 2,3,5,11, 331 is prime 332 :factors are 2,2,83,and is attractive 333 :factors are 3,3,37,and is attractive 334 :factors are 2,167,and is attractive 335 :factors are 5,67,and is attractive 336 :factors are 2,2,2,2,3,7, 337 is prime 338 :factors are 2,13,13,and is attractive 339 :factors are 3,113,and is attractive 340 :factors are 2,2,5,17, 341 :factors are 11,31,and is attractive 342 :factors are 2,3,3,19, 343 :factors are 7,7,7,and is attractive 344 :factors are 2,2,2,43, 345 :factors are 3,5,23,and is attractive 346 :factors are 2,173,and is attractive 347 is prime 348 :factors are 2,2,3,29, 349 is prime 350 :factors are 2,5,5,7, 351 :factors are 3,3,3,13, 352 :factors are 2,2,2,2,2,11, 353 is prime 354 :factors are 2,3,59,and is attractive 355 :factors are 5,71,and is attractive 356 :factors are 2,2,89,and is attractive 357 :factors are 3,7,17,and is attractive 358 :factors are 2,179,and is attractive 359 is prime 360 :factors are 2,2,2,3,3,5, 361 :factors are 19,19,and is attractive 362 :factors are 2,181,and is attractive 363 :factors are 3,11,11,and is attractive 364 :factors are 2,2,7,13, 365 :factors are 5,73,and is attractive 366 :factors are 2,3,61,and is attractive 367 is prime 368 :factors are 2,2,2,2,23,and is attractive 369 :factors are 3,3,41,and is attractive 370 :factors are 2,5,37,and is attractive 371 :factors are 7,53,and is attractive 372 :factors are 2,2,3,31, 373 is prime 374 :factors are 2,11,17,and is attractive 375 :factors are 3,5,5,5, 376 :factors are 2,2,2,47, 377 :factors are 13,29,and is attractive 378 :factors are 2,3,3,3,7,and is attractive 379 is prime 380 :factors are 2,2,5,19, 381 :factors are 3,127,and is attractive 382 :factors are 2,191,and is attractive 383 is prime 384 :factors are 2,2,2,2,2,2,2,3, 385 :factors are 5,7,11,and is attractive 386 :factors are 2,193,and is attractive 387 :factors are 3,3,43,and is attractive 388 :factors are 2,2,97,and is attractive 389 is prime 390 :factors are 2,3,5,13, 391 :factors are 17,23,and is attractive 392 :factors are 2,2,2,7,7,and is attractive 393 :factors are 3,131,and is attractive 394 :factors are 2,197,and is attractive 395 :factors are 5,79,and is attractive 396 :factors are 2,2,3,3,11,and is attractive 397 is prime 398 :factors are 2,199,and is attractive 399 :factors are 3,7,19,and is attractive 400 :factors are 2,2,2,2,5,5, 401 is prime 402 :factors are 2,3,67,and is attractive 403 :factors are 13,31,and is attractive 404 :factors are 2,2,101,and is attractive 405 :factors are 3,3,3,3,5,and is attractive 406 :factors are 2,7,29,and is attractive 407 :factors are 11,37,and is attractive 408 :factors are 2,2,2,3,17,and is attractive 409 is prime 410 :factors are 2,5,41,and is attractive 411 :factors are 3,137,and is attractive 412 :factors are 2,2,103,and is attractive 413 :factors are 7,59,and is attractive 414 :factors are 2,3,3,23, 415 :factors are 5,83,and is attractive 416 :factors are 2,2,2,2,2,13, 417 :factors are 3,139,and is attractive 418 :factors are 2,11,19,and is attractive 419 is prime 420 :factors are 2,2,3,5,7,and is attractive 421 is prime 422 :factors are 2,211,and is attractive 423 :factors are 3,3,47,and is attractive 424 :factors are 2,2,2,53, 425 :factors are 5,5,17,and is attractive 426 :factors are 2,3,71,and is attractive 427 :factors are 7,61,and is attractive 428 :factors are 2,2,107,and is attractive 429 :factors are 3,11,13,and is attractive 430 :factors are 2,5,43,and is attractive 431 is prime 432 :factors are 2,2,2,2,3,3,3,and is attractive 433 is prime 434 :factors are 2,7,31,and is attractive 435 :factors are 3,5,29,and is attractive 436 :factors are 2,2,109,and is attractive 437 :factors are 19,23,and is attractive 438 :factors are 2,3,73,and is attractive 439 is prime 440 :factors are 2,2,2,5,11,and is attractive 441 :factors are 3,3,7,7, 442 :factors are 2,13,17,and is attractive 443 is prime 444 :factors are 2,2,3,37, 445 :factors are 5,89,and is attractive 446 :factors are 2,223,and is attractive 447 :factors are 3,149,and is attractive 448 :factors are 2,2,2,2,2,2,7,and is attractive 449 is prime 450 :factors are 2,3,3,5,5,and is attractive 451 :factors are 11,41,and is attractive 452 :factors are 2,2,113,and is attractive 453 :factors are 3,151,and is attractive 454 :factors are 2,227,and is attractive 455 :factors are 5,7,13,and is attractive 456 :factors are 2,2,2,3,19,and is attractive 457 is prime 458 :factors are 2,229,and is attractive 459 :factors are 3,3,3,17, 460 :factors are 2,2,5,23, 461 is prime 462 :factors are 2,3,7,11, 463 is prime 464 :factors are 2,2,2,2,29,and is attractive 465 :factors are 3,5,31,and is attractive 466 :factors are 2,233,and is attractive 467 is prime 468 :factors are 2,2,3,3,13,and is attractive 469 :factors are 7,67,and is attractive 470 :factors are 2,5,47,and is attractive 471 :factors are 3,157,and is attractive 472 :factors are 2,2,2,59, 473 :factors are 11,43,and is attractive 474 :factors are 2,3,79,and is attractive 475 :factors are 5,5,19,and is attractive 476 :factors are 2,2,7,17, 477 :factors are 3,3,53,and is attractive 478 :factors are 2,239,and is attractive 479 is prime 480 :factors are 2,2,2,2,2,3,5,and is attractive 481 :factors are 13,37,and is attractive 482 :factors are 2,241,and is attractive 483 :factors are 3,7,23,and is attractive 484 :factors are 2,2,11,11, 485 :factors are 5,97,and is attractive 486 :factors are 2,3,3,3,3,3, 487 is prime 488 :factors are 2,2,2,61, 489 :factors are 3,163,and is attractive 490 :factors are 2,5,7,7, 491 is prime 492 :factors are 2,2,3,41, 493 :factors are 17,29,and is attractive 494 :factors are 2,13,19,and is attractive 495 :factors are 3,3,5,11, 496 :factors are 2,2,2,2,31,and is attractive 497 :factors are 7,71,and is attractive 498 :factors are 2,3,83,and is attractive 499 is prime 500 :factors are 2,2,5,5,5,and is attractive 501 :factors are 3,167,and is attractive 502 :factors are 2,251,and is attractive 503 is prime 504 :factors are 2,2,2,3,3,7, 505 :factors are 5,101,and is attractive 506 :factors are 2,11,23,and is attractive 507 :factors are 3,13,13,and is attractive 508 :factors are 2,2,127,and is attractive 509 is prime 510 :factors are 2,3,5,17, 511 :factors are 7,73,and is attractive 512 :factors are 2,2,2,2,2,2,2,2,2, 513 :factors are 3,3,3,19, 514 :factors are 2,257,and is attractive 515 :factors are 5,103,and is attractive 516 :factors are 2,2,3,43, 517 :factors are 11,47,and is attractive 518 :factors are 2,7,37,and is attractive 519 :factors are 3,173,and is attractive 520 :factors are 2,2,2,5,13,and is attractive 521 is prime 522 :factors are 2,3,3,29, 523 is prime 524 :factors are 2,2,131,and is attractive 525 :factors are 3,5,5,7, 526 :factors are 2,263,and is attractive 527 :factors are 17,31,and is attractive 528 :factors are 2,2,2,2,3,11, 529 :factors are 23,23,and is attractive 530 :factors are 2,5,53,and is attractive 531 :factors are 3,3,59,and is attractive 532 :factors are 2,2,7,19, 533 :factors are 13,41,and is attractive 534 :factors are 2,3,89,and is attractive 535 :factors are 5,107,and is attractive 536 :factors are 2,2,2,67, 537 :factors are 3,179,and is attractive 538 :factors are 2,269,and is attractive 539 :factors are 7,7,11,and is attractive 540 :factors are 2,2,3,3,3,5, 541 is prime 542 :factors are 2,271,and is attractive 543 :factors are 3,181,and is attractive 544 :factors are 2,2,2,2,2,17, 545 :factors are 5,109,and is attractive 546 :factors are 2,3,7,13, 547 is prime 548 :factors are 2,2,137,and is attractive 549 :factors are 3,3,61,and is attractive 550 :factors are 2,5,5,11, 551 :factors are 19,29,and is attractive 552 :factors are 2,2,2,3,23,and is attractive 553 :factors are 7,79,and is attractive 554 :factors are 2,277,and is attractive 555 :factors are 3,5,37,and is attractive 556 :factors are 2,2,139,and is attractive 557 is prime 558 :factors are 2,3,3,31, 559 :factors are 13,43,and is attractive 560 :factors are 2,2,2,2,5,7, 561 :factors are 3,11,17,and is attractive 562 :factors are 2,281,and is attractive 563 is prime 564 :factors are 2,2,3,47, 565 :factors are 5,113,and is attractive 566 :factors are 2,283,and is attractive 567 :factors are 3,3,3,3,7,and is attractive 568 :factors are 2,2,2,71, 569 is prime 570 :factors are 2,3,5,19, 571 is prime 572 :factors are 2,2,11,13, 573 :factors are 3,191,and is attractive 574 :factors are 2,7,41,and is attractive 575 :factors are 5,5,23,and is attractive 576 :factors are 2,2,2,2,2,2,3,3, 577 is prime 578 :factors are 2,17,17,and is attractive 579 :factors are 3,193,and is attractive 580 :factors are 2,2,5,29, 581 :factors are 7,83,and is attractive 582 :factors are 2,3,97,and is attractive 583 :factors are 11,53,and is attractive 584 :factors are 2,2,2,73, 585 :factors are 3,3,5,13, 586 :factors are 2,293,and is attractive 587 is prime 588 :factors are 2,2,3,7,7,and is attractive 589 :factors are 19,31,and is attractive 590 :factors are 2,5,59,and is attractive 591 :factors are 3,197,and is attractive 592 :factors are 2,2,2,2,37,and is attractive 593 is prime 594 :factors are 2,3,3,3,11,and is attractive 595 :factors are 5,7,17,and is attractive 596 :factors are 2,2,149,and is attractive 597 :factors are 3,199,and is attractive 598 :factors are 2,13,23,and is attractive 599 is prime 600 :factors are 2,2,2,3,5,5, 601 is prime 602 :factors are 2,7,43,and is attractive 603 :factors are 3,3,67,and is attractive 604 :factors are 2,2,151,and is attractive 605 :factors are 5,11,11,and is attractive 606 :factors are 2,3,101,and is attractive 607 is prime 608 :factors are 2,2,2,2,2,19, 609 :factors are 3,7,29,and is attractive 610 :factors are 2,5,61,and is attractive 611 :factors are 13,47,and is attractive 612 :factors are 2,2,3,3,17,and is attractive 613 is prime 614 :factors are 2,307,and is attractive 615 :factors are 3,5,41,and is attractive 616 :factors are 2,2,2,7,11,and is attractive 617 is prime 618 :factors are 2,3,103,and is attractive 619 is prime 620 :factors are 2,2,5,31, 621 :factors are 3,3,3,23, 622 :factors are 2,311,and is attractive 623 :factors are 7,89,and is attractive 624 :factors are 2,2,2,2,3,13, 625 :factors are 5,5,5,5, 626 :factors are 2,313,and is attractive 627 :factors are 3,11,19,and is attractive 628 :factors are 2,2,157,and is attractive 629 :factors are 17,37,and is attractive 630 :factors are 2,3,3,5,7,and is attractive 631 is prime 632 :factors are 2,2,2,79, 633 :factors are 3,211,and is attractive 634 :factors are 2,317,and is attractive 635 :factors are 5,127,and is attractive 636 :factors are 2,2,3,53, 637 :factors are 7,7,13,and is attractive 638 :factors are 2,11,29,and is attractive 639 :factors are 3,3,71,and is attractive 640 :factors are 2,2,2,2,2,2,2,5, 641 is prime 642 :factors are 2,3,107,and is attractive 643 is prime 644 :factors are 2,2,7,23, 645 :factors are 3,5,43,and is attractive 646 :factors are 2,17,19,and is attractive 647 is prime 648 :factors are 2,2,2,3,3,3,3,and is attractive 649 :factors are 11,59,and is attractive 650 :factors are 2,5,5,13, 651 :factors are 3,7,31,and is attractive 652 :factors are 2,2,163,and is attractive 653 is prime 654 :factors are 2,3,109,and is attractive 655 :factors are 5,131,and is attractive 656 :factors are 2,2,2,2,41,and is attractive 657 :factors are 3,3,73,and is attractive 658 :factors are 2,7,47,and is attractive 659 is prime 660 :factors are 2,2,3,5,11,and is attractive 661 is prime 662 :factors are 2,331,and is attractive 663 :factors are 3,13,17,and is attractive 664 :factors are 2,2,2,83, 665 :factors are 5,7,19,and is attractive 666 :factors are 2,3,3,37, 667 :factors are 23,29,and is attractive 668 :factors are 2,2,167,and is attractive 669 :factors are 3,223,and is attractive 670 :factors are 2,5,67,and is attractive 671 :factors are 11,61,and is attractive 672 :factors are 2,2,2,2,2,3,7,and is attractive 673 is prime 674 :factors are 2,337,and is attractive 675 :factors are 3,3,3,5,5,and is attractive 676 :factors are 2,2,13,13, 677 is prime 678 :factors are 2,3,113,and is attractive 679 :factors are 7,97,and is attractive 680 :factors are 2,2,2,5,17,and is attractive 681 :factors are 3,227,and is attractive 682 :factors are 2,11,31,and is attractive 683 is prime 684 :factors are 2,2,3,3,19,and is attractive 685 :factors are 5,137,and is attractive 686 :factors are 2,7,7,7, 687 :factors are 3,229,and is attractive 688 :factors are 2,2,2,2,43,and is attractive 689 :factors are 13,53,and is attractive 690 :factors are 2,3,5,23, 691 is prime 692 :factors are 2,2,173,and is attractive 693 :factors are 3,3,7,11, 694 :factors are 2,347,and is attractive 695 :factors are 5,139,and is attractive 696 :factors are 2,2,2,3,29,and is attractive 697 :factors are 17,41,and is attractive 698 :factors are 2,349,and is attractive 699 :factors are 3,233,and is attractive 700 :factors are 2,2,5,5,7,and is attractive 701 is prime 702 :factors are 2,3,3,3,13,and is attractive 703 :factors are 19,37,and is attractive 704 :factors are 2,2,2,2,2,2,11,and is attractive 705 :factors are 3,5,47,and is attractive 706 :factors are 2,353,and is attractive 707 :factors are 7,101,and is attractive 708 :factors are 2,2,3,59, 709 is prime 710 :factors are 2,5,71,and is attractive 711 :factors are 3,3,79,and is attractive 712 :factors are 2,2,2,89, 713 :factors are 23,31,and is attractive 714 :factors are 2,3,7,17, 715 :factors are 5,11,13,and is attractive 716 :factors are 2,2,179,and is attractive 717 :factors are 3,239,and is attractive 718 :factors are 2,359,and is attractive 719 is prime 720 :factors are 2,2,2,2,3,3,5,and is attractive 721 :factors are 7,103,and is attractive 722 :factors are 2,19,19,and is attractive 723 :factors are 3,241,and is attractive 724 :factors are 2,2,181,and is attractive 725 :factors are 5,5,29,and is attractive 726 :factors are 2,3,11,11, 727 is prime 728 :factors are 2,2,2,7,13,and is attractive 729 :factors are 3,3,3,3,3,3, 730 :factors are 2,5,73,and is attractive 731 :factors are 17,43,and is attractive 732 :factors are 2,2,3,61, 733 is prime 734 :factors are 2,367,and is attractive 735 :factors are 3,5,7,7, 736 :factors are 2,2,2,2,2,23, 737 :factors are 11,67,and is attractive 738 :factors are 2,3,3,41, 739 is prime 740 :factors are 2,2,5,37, 741 :factors are 3,13,19,and is attractive 742 :factors are 2,7,53,and is attractive 743 is prime 744 :factors are 2,2,2,3,31,and is attractive 745 :factors are 5,149,and is attractive 746 :factors are 2,373,and is attractive 747 :factors are 3,3,83,and is attractive 748 :factors are 2,2,11,17, 749 :factors are 7,107,and is attractive 750 :factors are 2,3,5,5,5,and is attractive 751 is prime 752 :factors are 2,2,2,2,47,and is attractive 753 :factors are 3,251,and is attractive 754 :factors are 2,13,29,and is attractive 755 :factors are 5,151,and is attractive 756 :factors are 2,2,3,3,3,7, 757 is prime 758 :factors are 2,379,and is attractive 759 :factors are 3,11,23,and is attractive 760 :factors are 2,2,2,5,19,and is attractive 761 is prime 762 :factors are 2,3,127,and is attractive 763 :factors are 7,109,and is attractive 764 :factors are 2,2,191,and is attractive 765 :factors are 3,3,5,17, 766 :factors are 2,383,and is attractive 767 :factors are 13,59,and is attractive 768 :factors are 2,2,2,2,2,2,2,2,3, 769 is prime 770 :factors are 2,5,7,11, 771 :factors are 3,257,and is attractive 772 :factors are 2,2,193,and is attractive 773 is prime 774 :factors are 2,3,3,43, 775 :factors are 5,5,31,and is attractive 776 :factors are 2,2,2,97, 777 :factors are 3,7,37,and is attractive 778 :factors are 2,389,and is attractive 779 :factors are 19,41,and is attractive 780 :factors are 2,2,3,5,13,and is attractive 781 :factors are 11,71,and is attractive 782 :factors are 2,17,23,and is attractive 783 :factors are 3,3,3,29, 784 :factors are 2,2,2,2,7,7, 785 :factors are 5,157,and is attractive 786 :factors are 2,3,131,and is attractive 787 is prime 788 :factors are 2,2,197,and is attractive 789 :factors are 3,263,and is attractive 790 :factors are 2,5,79,and is attractive 791 :factors are 7,113,and is attractive 792 :factors are 2,2,2,3,3,11, 793 :factors are 13,61,and is attractive 794 :factors are 2,397,and is attractive 795 :factors are 3,5,53,and is attractive 796 :factors are 2,2,199,and is attractive 797 is prime 798 :factors are 2,3,7,19, 799 :factors are 17,47,and is attractive 800 :factors are 2,2,2,2,2,5,5,and is attractive 801 :factors are 3,3,89,and is attractive 802 :factors are 2,401,and is attractive 803 :factors are 11,73,and is attractive 804 :factors are 2,2,3,67, 805 :factors are 5,7,23,and is attractive 806 :factors are 2,13,31,and is attractive 807 :factors are 3,269,and is attractive 808 :factors are 2,2,2,101, 809 is prime 810 :factors are 2,3,3,3,3,5, 811 is prime 812 :factors are 2,2,7,29, 813 :factors are 3,271,and is attractive 814 :factors are 2,11,37,and is attractive 815 :factors are 5,163,and is attractive 816 :factors are 2,2,2,2,3,17, 817 :factors are 19,43,and is attractive 818 :factors are 2,409,and is attractive 819 :factors are 3,3,7,13, 820 :factors are 2,2,5,41, 821 is prime 822 :factors are 2,3,137,and is attractive 823 is prime 824 :factors are 2,2,2,103, 825 :factors are 3,5,5,11, 826 :factors are 2,7,59,and is attractive 827 is prime 828 :factors are 2,2,3,3,23,and is attractive 829 is prime 830 :factors are 2,5,83,and is attractive 831 :factors are 3,277,and is attractive 832 :factors are 2,2,2,2,2,2,13,and is attractive 833 :factors are 7,7,17,and is attractive 834 :factors are 2,3,139,and is attractive 835 :factors are 5,167,and is attractive 836 :factors are 2,2,11,19, 837 :factors are 3,3,3,31, 838 :factors are 2,419,and is attractive 839 is prime 840 :factors are 2,2,2,3,5,7, 841 :factors are 29,29,and is attractive 842 :factors are 2,421,and is attractive 843 :factors are 3,281,and is attractive 844 :factors are 2,2,211,and is attractive 845 :factors are 5,13,13,and is attractive 846 :factors are 2,3,3,47, 847 :factors are 7,11,11,and is attractive 848 :factors are 2,2,2,2,53,and is attractive 849 :factors are 3,283,and is attractive 850 :factors are 2,5,5,17, 851 :factors are 23,37,and is attractive 852 :factors are 2,2,3,71, 853 is prime 854 :factors are 2,7,61,and is attractive 855 :factors are 3,3,5,19, 856 :factors are 2,2,2,107, 857 is prime 858 :factors are 2,3,11,13, 859 is prime 860 :factors are 2,2,5,43, 861 :factors are 3,7,41,and is attractive 862 :factors are 2,431,and is attractive 863 is prime 864 :factors are 2,2,2,2,2,3,3,3, 865 :factors are 5,173,and is attractive 866 :factors are 2,433,and is attractive 867 :factors are 3,17,17,and is attractive 868 :factors are 2,2,7,31, 869 :factors are 11,79,and is attractive 870 :factors are 2,3,5,29, 871 :factors are 13,67,and is attractive 872 :factors are 2,2,2,109, 873 :factors are 3,3,97,and is attractive 874 :factors are 2,19,23,and is attractive 875 :factors are 5,5,5,7, 876 :factors are 2,2,3,73, 877 is prime 878 :factors are 2,439,and is attractive 879 :factors are 3,293,and is attractive 880 :factors are 2,2,2,2,5,11, 881 is prime 882 :factors are 2,3,3,7,7,and is attractive 883 is prime 884 :factors are 2,2,13,17, 885 :factors are 3,5,59,and is attractive 886 :factors are 2,443,and is attractive 887 is prime 888 :factors are 2,2,2,3,37,and is attractive 889 :factors are 7,127,and is attractive 890 :factors are 2,5,89,and is attractive 891 :factors are 3,3,3,3,11,and is attractive 892 :factors are 2,2,223,and is attractive 893 :factors are 19,47,and is attractive 894 :factors are 2,3,149,and is attractive 895 :factors are 5,179,and is attractive 896 :factors are 2,2,2,2,2,2,2,7, 897 :factors are 3,13,23,and is attractive 898 :factors are 2,449,and is attractive 899 :factors are 29,31,and is attractive 900 :factors are 2,2,3,3,5,5, 901 :factors are 17,53,and is attractive 902 :factors are 2,11,41,and is attractive 903 :factors are 3,7,43,and is attractive 904 :factors are 2,2,2,113, 905 :factors are 5,181,and is attractive 906 :factors are 2,3,151,and is attractive 907 is prime 908 :factors are 2,2,227,and is attractive 909 :factors are 3,3,101,and is attractive 910 :factors are 2,5,7,13, 911 is prime 912 :factors are 2,2,2,2,3,19, 913 :factors are 11,83,and is attractive 914 :factors are 2,457,and is attractive 915 :factors are 3,5,61,and is attractive 916 :factors are 2,2,229,and is attractive 917 :factors are 7,131,and is attractive 918 :factors are 2,3,3,3,17,and is attractive 919 is prime 920 :factors are 2,2,2,5,23,and is attractive 921 :factors are 3,307,and is attractive 922 :factors are 2,461,and is attractive 923 :factors are 13,71,and is attractive 924 :factors are 2,2,3,7,11,and is attractive 925 :factors are 5,5,37,and is attractive 926 :factors are 2,463,and is attractive 927 :factors are 3,3,103,and is attractive 928 :factors are 2,2,2,2,2,29, 929 is prime 930 :factors are 2,3,5,31, 931 :factors are 7,7,19,and is attractive 932 :factors are 2,2,233,and is attractive 933 :factors are 3,311,and is attractive 934 :factors are 2,467,and is attractive 935 :factors are 5,11,17,and is attractive 936 :factors are 2,2,2,3,3,13, 937 is prime 938 :factors are 2,7,67,and is attractive 939 :factors are 3,313,and is attractive 940 :factors are 2,2,5,47, 941 is prime 942 :factors are 2,3,157,and is attractive 943 :factors are 23,41,and is attractive 944 :factors are 2,2,2,2,59,and is attractive 945 :factors are 3,3,3,5,7,and is attractive 946 :factors are 2,11,43,and is attractive 947 is prime 948 :factors are 2,2,3,79, 949 :factors are 13,73,and is attractive 950 :factors are 2,5,5,19, 951 :factors are 3,317,and is attractive 952 :factors are 2,2,2,7,17,and is attractive 953 is prime 954 :factors are 2,3,3,53, 955 :factors are 5,191,and is attractive 956 :factors are 2,2,239,and is attractive 957 :factors are 3,11,29,and is attractive 958 :factors are 2,479,and is attractive 959 :factors are 7,137,and is attractive 960 :factors are 2,2,2,2,2,2,3,5, 961 :factors are 31,31,and is attractive 962 :factors are 2,13,37,and is attractive 963 :factors are 3,3,107,and is attractive 964 :factors are 2,2,241,and is attractive 965 :factors are 5,193,and is attractive 966 :factors are 2,3,7,23, 967 is prime 968 :factors are 2,2,2,11,11,and is attractive 969 :factors are 3,17,19,and is attractive 970 :factors are 2,5,97,and is attractive 971 is prime 972 :factors are 2,2,3,3,3,3,3,and is attractive 973 :factors are 7,139,and is attractive 974 :factors are 2,487,and is attractive 975 :factors are 3,5,5,13, 976 :factors are 2,2,2,2,61,and is attractive 977 is prime 978 :factors are 2,3,163,and is attractive 979 :factors are 11,89,and is attractive 980 :factors are 2,2,5,7,7,and is attractive 981 :factors are 3,3,109,and is attractive 982 :factors are 2,491,and is attractive 983 is prime 984 :factors are 2,2,2,3,41,and is attractive 985 :factors are 5,197,and is attractive 986 :factors are 2,17,29,and is attractive 987 :factors are 3,7,47,and is attractive 988 :factors are 2,2,13,19, 989 :factors are 23,43,and is attractive 990 :factors are 2,3,3,5,11,and is attractive 991 is prime 992 :factors are 2,2,2,2,2,31, 993 :factors are 3,331,and is attractive 994 :factors are 2,7,71,and is attractive 995 :factors are 5,199,and is attractive 996 :factors are 2,2,3,83, 997 is prime 998 :factors are 2,499,and is attractive 999 :factors are 3,3,3,37, 1000 :factors are 2,2,2,5,5,5,