A000790 question

T. D. Noe noe at sspectra.com
Fri Jun 10 19:20:27 CEST 2005


>I was looking at the including the range of A000790 (the primary pretenders)
>in the OEIS.  According to http://www.research.att.com/~njas/doc/guy.ps, the
>range of A000790 is finite with 132 values.  A long-winded description of
>these values is given on page 3, which boils down to numbers of the form pq
>< 561 where primes p, q satisfy q == 1 (mod p-1).
>
>I computed these numbers directly from the article description as well as
>from my simplified definition, and in each case I got the following 131
>numbers:
>
>4 6 9 10 14 15 21 22 25 26 33 34 38 39 46 49 51 57 58 62 65 69 74 82 85
>86 87 91 93 94 106 111 118 121 122 123 129 133 134 141 142 145 146 158
>159 166 169 177 178 183 185 194 201 202 205 206 213 214 217 218 219 226
>237 249 254 259 262 265 267 274 278 289 291 298 301 302 303 305 309 314
>321 326 327 334 339 341 346 358 361 362 365 381 382 386 393 394 398 411
>417 422 427 445 446 447 451 453 454 458 466 469 471 478 481 482 485 489
>501 502 505 511 514 519 526 529 537 538 542 543 545 553 554
>
>So how many of these numbers are there, 131 or 132?


The table in the paper lists 561 also because it is the least Carmichael
number; if no smaller power works, 561 will.

Tony






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