This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A066100 #39 Dec 14 2024 20:30:53
%S A066100 2,3,11,191,269,383,509,809,827,887,1409,1427,1787,1907,1949,2141,
%T A066100 2243,2339,2357,2477,2591,2699,2789,4073,4517,4643,4787,5171,5237,
%U A066100 5501,5531,5693,6311,6329,6359,6911,6947,7019,7253,7349,7499,7577,7691,7907,8819
%N A066100 Primes p such that p^6 + p^3 + 1 is prime.
%C A066100 Original name: "Primes p such that the sum of the cubes of the divisors of p^2 is prime."
%C A066100 Primes p such that sigma_3(p^2) is prime.
%C A066100 It appears that squares of these primes give A063783, those numbers whose sum of cubes of divisors is prime.
%H A066100 Amiram Eldar, <a href="/A066100/b066100.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%H A066100 Paolo Santonastaso and Ferdinando Zullo, <a href="https://doi.org/10.1016/j.jpaa.2021.106842">Linearized trinomials with maximum kernel</a>, Journal of Pure and Applied Algebra, Vol. 226, No. 3 (2022), 106842; <a href="https://arxiv.org/abs/2012.14861">arXiv preprint</a>, arXiv:2012.14861 [math.NT], 2020-2021.
%F A066100 a(n) = sqrt(A063783(n)). - _Amiram Eldar_, Aug 16 2024
%e A066100 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 A066100 Select[Prime@ Range@ 1200, PrimeQ@ DivisorSigma[3, #^2] &] (* _Michael De Vlieger_, Jul 16 2017 *)
%o A066100 (PARI) isok(p) = { isprime(p) && isprime(sigma(p^2, 3)) } \\ _Harry J. Smith_, Nov 13 2009
%Y A066100 Cf. A000040, A001158, A063783.
%K A066100 nonn
%O A066100 1,1
%A A066100 _Labos Elemer_, Dec 04 2001
%E A066100 Name replaced with simpler description offered in an Oct 10 2010 comment by _James R. Buddenhagen_ by _Jon E. Schoenfield_, Jul 17 2017