A102328 Primes p such that the largest prime divisor of p^6 + 1 is less than p.

30977, 69127, 104681, 109807, 114671, 141637, 146057, 160319, 160639, 170371, 171169, 176087, 211723, 216119, 217081, 319321, 381673, 389083, 390151, 416219, 437401, 484609, 492257, 525571, 564713, 565241, 574127, 591601, 612173, 621259

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Formula

Solutions to {A006530(p^6+1) < p} where p is a prime number.

Example

p = 30977, p^6 + 1 = 883560179055825771003237890 = 2*5*13*37*61*113*181*13921*18517*22189*25741, so the largest prime factor is 25741 < p = 30977.

Mathematica

Select[Prime[Range[60000]], Max[PrimeFactorList[1 + #^6]] < # &] (* Ray Chandler, Jan 08 2005 *)

Prog

(PARI) is(k) = isprime(k) && vecmax(factor(k^6+1)[, 1]) < k; \\ Amiram Eldar, Jun 21 2024

Crossrefs

Cf. A000040, A006530, A065091, A073501, A102327.

Sequence in context: A338948 A186918 A185802 * A157111 A236976 A143162

Adjacent sequences: A102325 A102326 A102327 * A102329 A102330 A102331

Keyword

nonn

Author

Labos Elemer, Jan 05 2005

Extensions

Extended by Ray Chandler, Jan 08 2005

Status

approved