cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A341665 Primes p such that p^5 - 1 has 8 divisors.

Original entry on oeis.org

7, 23, 83, 227, 263, 359, 479, 503, 563, 1187, 2999, 3803, 4703, 4787, 4919, 5939, 6599, 8819, 10667, 14159, 16139, 16187, 18119, 21227, 22943, 25847, 26003, 26903, 27827, 29123, 29339, 29663, 36263, 43403, 44519, 44963, 46199, 47123, 48947, 49103, 49499
Offset: 1

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Author

Jon E. Schoenfield, Feb 26 2021

Keywords

Comments

For each term p, p^5 - 1 = (p-1)*(p^4 + p^3 + p^2 + p + 1) is a number of the form 2*q*r (where q and r are distinct primes): p-1 = 2*q and p^4 + p^3 + p^2 + p + 1 = r.
Conjecture: sequence is infinite.

Examples

			     p =                       factorization
  n  a(n)      p^5 - 1          of (p^5 - 1)
  -  ----  --------------  ---------------------
  1     7           16806  2 *   3 *        2801
  2    23         6436342  2 *  11 *      292561
  3    83      3939040642  2 *  41 *    48037081
  4   227    602738989906  2 * 113 *  2666986681
  5   263   1258284197542  2 * 131 *  4802611441
  6   359   5963102065798  2 * 179 * 16656709681
  7   479  25216079618398  2 * 239 * 52753304641
  8   503  32198817702742  2 * 251 * 64141071121
  ...
		

Crossrefs

Programs

  • Mathematica
    Select[Range[50000], PrimeQ[#] && DivisorSigma[0, #^5 - 1] == 8 &] (* Amiram Eldar, Feb 26 2021 *)
  • PARI
    isok(p) = isprime(p) && (numdiv(p^5-1) == 8); \\ Michel Marcus, Feb 26 2021
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