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%I #25 Apr 17 2021 01:43:04
%S 2,3,11,191,269,383,509,809,827,887,1409,1427,1787,1907,1949,2141,
%T 2243,2339,2357,2477,2591,2699,2789,4073,4517,4643,4787,5171,5237,
%U 5501,5531,5693,6311,6329,6359,6911,6947,7019,7253,7349,7499,7577,7691,7907,8819
%N Primes p such that p^6 + p^3 + 1 is prime.
%C Original name: "Primes p such that the sum of the cubes of the divisors of p^2 is prime."
%C It appears that squares of these primes give A063783, those numbers whose sum of cubes of divisors is prime.
%H Harry J. Smith, <a href="/A066100/b066100.txt">Table of n, a(n) for n=1..1000</a>
%H Paolo Santonastaso and Ferdinando Zullo, <a href="https://arxiv.org/abs/2012.14861">Linearized trinomials with maximum kernel</a>, arXiv:2012.14861 [math.NT], 2020.
%F Primes p such that sigma_3(p^2) is prime.
%e 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.
%t Select[Prime@ Range@ 1200, PrimeQ@ DivisorSigma[3, #^2] &] (* _Michael De Vlieger_, Jul 16 2017 *)
%o (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
%Y Cf. A000040, A001158, A063783.
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 04 2001
%E Name replaced with simpler description offered in an Oct 10 2010 comment by _James R. Buddenhagen_ by _Jon E. Schoenfield_, Jul 17 2017
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