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

1,1

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.

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.

Formula

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

Example

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.

Mathematica

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

Prog

(PARI) { n=0; for (m=1, 10^9, p=prime(m); if (isprime(sigma(p^2, 3)), write("b066100.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 13 2009

Crossrefs

Cf. A000040, A001158, A063783.

Sequence in context: A177854 A273598 A135161 * A029497 A318130 A109809

Adjacent sequences: A066097 A066098 A066099 * A066101 A066102 A066103

Keyword

nonn

Author

Labos Elemer, Dec 04 2001

Extensions

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

Status

approved