A342063 Primes p such that p^8 - 1 has fewer than 384 divisors.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 61, 71

Offset

1,1

Comments

For all primes p > 71, p^8 - 1 has at least A309906(8)=384 divisors.

Links

Table of n, a(n) for n=1..12.

Example

      p =
   n  a(n)        factorization of p^8 - 1         a(n)
  --  ----  -------------------------------------  ----
   1    2         3   * 5   * 17                      8
   2    3   2^5       * 5   * 41                     24
   3    5   2^5 * 3         * 13 * 313               48
   4    7   2^6 * 3   * 5^2 * 1201                   84
   5   11   2^5 * 3   * 5   * 61 * 7321              96
   6   13   2^5 * 3   * 5   * 7 * 17 * 14281        192
   7   17   2^7 * 3^2 * 5   * 29 * 41761            192
   8   19   2^5 * 3^2 * 5   * 17 * 181 * 3833       288
   9   23   2^6 * 3   * 5   * 11 * 53 * 139921      224
  10   29   2^5 * 3   * 5   * 7 * 421 * 353641      192
  11   61   2^5 * 3   * 5   * 31 * 1861 * 6922921   192
  12   71   2^6 * 3^2 * 5   * 7 * 2521 * 12705841   336

Crossrefs

Cf. A000005, A000040, A309906, A342062, A342064.

Sequence in context: A279956 A197300 A028864 * A067903 A341934 A224229

Adjacent sequences: A342060 A342061 A342062 * A342064 A342065 A342066

Keyword

nonn,fini,full

Author

Jon E. Schoenfield, Feb 27 2021

Status

approved