A066100 Primes p such that p^6 + p^3 + 1 is prime.

2, 3, 11, 191, 269, 383, 509, 809, 827, 887, 1409, 1427, 1787, 1907, 1949, 2141, 2243, 2339, 2357, 2477, 2591, 2699, 2789, 4073, 4517, 4643, 4787, 5171, 5237, 5501, 5531, 5693, 6311, 6329, 6359, 6911, 6947, 7019, 7253, 7349, 7499, 7577, 7691, 7907, 8819

Offset: 1

Author

Labos Elemer, Dec 04 2001

Keywords

• nonn

Comments

Original name: "Primes p such that the sum of the cubes of the divisors of p^2 is prime."

Primes p such that sigma_3(p^2) is prime.

It appears that squares of these primes give A063783, those numbers whose sum of cubes of divisors is prime.

Examples

			p=11: p^2=121, cubes of divisors of p^2 = {p^6, p^3, 1}, sigma_3(p^2) = p^6 + p^3 + 1 = 1771561 + 1331 + 1 = 1772893 = q, a prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
• Paolo Santonastaso and Ferdinando Zullo, Linearized trinomials with maximum kernel, Journal of Pure and Applied Algebra, Vol. 226, No. 3 (2022), 106842; arXiv preprint, arXiv:2012.14861 [math.NT], 2020-2021.

Crossrefs

Cf. A000040, A001158, A063783.

Programs

Mathematica

Select[Prime@ Range@ 1200, PrimeQ@ DivisorSigma[3, #^2] &] (* Michael De Vlieger, Jul 16 2017 *)

PARI

isok(p) = { isprime(p) && isprime(sigma(p^2, 3)) } \\ Harry J. Smith, Nov 13 2009

Formula

a(n) = sqrt(A063783(n)). - Amiram Eldar, Aug 16 2024

Extensions

Name replaced with simpler description offered in an Oct 10 2010 comment by James R. Buddenhagen by Jon E. Schoenfield, Jul 17 2017