# This b-file was computed by Antti Karttunen, 2024-11-14 # in GP/PARI CALCULATOR Version 2.9.4 (released) amd64 running linux (x86-64/GMP-6.1.2 kernel) 64-bit version, compiled: Dec 19 2017, gcc version 7.3.0 (Ubuntu 7.3.0-1ubuntu1), threading engine: pthread # with the following program: # # up_to = (2*210)-1; \\ The primorial base expansion of up_to must be "full" (maximal digits), apart from the most significant digit. # A002110(n) = prod(i=1,n,prime(i)); # A276085(n) = { my(f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= prime(i); i++); s += f[k, 2]*pr); (s); }; # A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); }; # A359550(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(0)); if(pp > n, return(1))); }; # A376411list(up_to) = { my(size=up_to, v=vector(size), m=A276086(size), s=1, j); for(i=2,m,if(!(m%i), j=A276085(i); v[j] = s; print1("i=",i," v[",j,"]=",s", ");); s += A359550(i)); (v); }; # v376411 = A376411list(up_to); # A376411(n) = if(!n,n,v376411[n]); # for(n=0,up_to,write("b376411_upto419.txt", n, " ", A376411(n))); 0 0 1 1 2 2 3 4 4 6 5 13 6 3 7 7 8 11 9 21 10 32 11 64 12 18 13 36 14 54 15 108 16 162 17 325 18 90 19 180 20 271 21 541 22 812 23 1624 24 450 25 902 26 1354 27 2707 28 4061 29 8122 30 5 31 10 32 15 33 30 34 45 35 91 36 25 37 50 38 75 39 151 40 227 41 454 42 126 43 253 44 378 45 758 46 1137 47 2274 48 632 49 1264 50 1895 51 3790 52 5685 53 11370 54 3158 55 6317 56 9475 57 18952 58 28428 59 56856 60 35 61 70 62 106 63 212 64 318 65 637 66 176 67 353 68 530 69 1061 70 1592 71 3183 72 884 73 1769 74 2653 75 5306 76 7959 77 15919 78 4422 79 8844 80 13267 81 26532 82 39799 83 79598 84 22110 85 44221 86 66333 87 132666 88 198999 89 397998 90 248 91 495 92 742 93 1486 94 2229 95 4458 96 1238 97 2475 98 3714 99 7428 100 11144 101 22287 102 6191 103 12381 104 18573 105 37146 106 55719 107 111439 108 30955 109 61910 110 92865 111 185732 112 278597 113 557196 114 154777 115 309553 116 464330 117 928660 118 1392989 119 2785980 120 1734 121 3467 122 5200 123 10401 124 15601 125 31203 126 8667 127 17334 128 26002 129 52003 130 78007 131 156014 132 43335 133 86674 134 130013 135 260024 136 390038 137 780074 138 216687 139 433375 140 650061 141 1300123 142 1950185 143 3900371 144 1083436 145 2166873 146 3250310 147 6500619 148 9750929 149 19501859 150 12134 151 24269 152 36402 153 72807 154 109210 155 218422 156 60672 157 121345 158 182017 159 364034 160 546051 161 1092103 162 303361 163 606724 164 910085 165 1820172 166 2730259 167 5460520 168 1516810 169 3033622 170 4550433 171 9100866 172 13651300 173 27302601 174 7584056 175 15168111 176 22752168 177 45504337 178 68256505 179 136513010 180 84941 181 169882 182 254825 183 509649 184 764472 185 1528946 186 424707 187 849414 188 1274121 189 2548242 190 3822363 191 7644728 192 2123534 193 4247070 194 6370606 195 12741213 196 19111821 197 38223644 198 10617678 199 21235356 200 31853036 201 63706070 202 95559107 203 191118214 204 53088394 205 106176786 206 159265179 207 318530358 208 477795538 209 955591077 210 8 211 16 212 23 213 47 214 71 215 142 216 39 217 79 218 118 219 238 220 357 221 715 222 198 223 397 224 595 225 1191 226 1787 227 3573 228 993 229 1986 230 2978 231 5956 232 8934 233 17869 234 4963 235 9927 236 14890 237 29781 238 44672 239 89345 240 55 241 111 242 167 243 333 244 500 245 1000 246 277 247 556 248 834 249 1668 250 2501 251 5003 252 1389 253 2779 254 4170 255 8338 256 12508 257 25015 258 6948 259 13898 260 20847 261 41694 262 62542 263 125085 264 34744 265 69492 266 104236 267 208475 268 312712 269 625423 270 389 271 778 272 1167 273 2334 274 3502 275 7003 276 1946 277 3891 278 5836 279 11674 280 17511 281 35023 282 9728 283 19457 284 29186 285 58372 286 87559 287 175118 288 48643 289 97287 290 145932 291 291864 292 437797 293 875594 294 243221 295 486441 296 729660 297 1459322 298 2188983 299 4377967 300 2723 301 5447 302 8171 303 16343 304 24516 305 49032 306 13619 307 27240 308 40860 309 81722 310 122583 311 245167 312 68101 313 136203 314 204306 315 408610 316 612915 317 1225829 318 340508 319 681017 320 1021526 321 2043051 322 3064577 323 6129155 324 1702543 325 3405086 326 5107630 327 10215258 328 15322888 329 30645777 330 19068 331 38137 332 57204 333 114410 334 171616 335 343232 336 95342 337 190686 338 286027 339 572055 340 858082 341 1716164 342 476712 343 953424 344 1430136 345 2860272 346 4290408 347 8580815 348 2383561 349 4767121 350 7150680 351 14301362 352 21452044 353 42904089 354 11917802 355 23835605 356 35753407 357 71506814 358 107260222 359 214520445 360 133478 361 266958 362 400439 363 800876 364 1201314 365 2402629 366 667396 367 1334793 368 2002189 369 4004381 370 6006571 371 12013145 372 3336983 373 6673968 374 10010953 375 20021907 376 30032861 377 60065724 378 16684922 379 33369847 380 50054771 381 100109542 382 150164312 383 300328624 384 83424617 385 166849236 386 250273854 387 500547707 388 750821560 389 1501643120 390 934355 391 1868710 392 2803067 393 5606134 394 8409200 395 16818402 396 4671777 397 9343556 398 14015334 399 28030670 400 42046007 401 84092014 402 23358893 403 46717785 404 70076678 405 140153356 406 210230037 407 420460073 408 116794466 409 233588930 410 350383395 411 700766790 412 1051150184 413 2102300370 414 583972324 415 1167944648 416 1751916973 417 3503833950 418 5255750924 419 10511501849