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 A353886 #15 Dec 11 2023 08:36:56
%S A353886 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,23,24,25,26,27,
%T A353886 28,29,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U A353886 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,69,70,71,72
%N A353886 Nonnegative numbers k such that k^2 + k + 1 is squarefree.
%C A353886 Dimitrov proved that this sequence is infinite.
%C A353886 The number of terms not exceeding X is Product_{p prime} (1 - A000086(p)/p^2) * X + O(X^(4/5+eps)) (Dimitrov, 2023). The coefficient of X, which is the asymptotic density of this sequence, equals Product_{primes p == 1 (mod 3)} (1 - 2/p^2) = 0.93484201367... . - _Amiram Eldar_, Dec 11 2023
%H A353886 Amiram Eldar, <a href="/A353886/b353886.txt">Table of n, a(n) for n = 1..10000</a>
%H A353886 Stoyan Ivanov Dimitrov, <a href="https://doi.org/10.1515/gmj-2023-2010">Square-free values of n^2+n+1</a>, Georgian Mathematical Journal, Vol. 30, No. 3 (2023), pp. 333-348; <a href="https://arxiv.org/abs/2205.02488">arXiv preprint</a>, arXiv:2205.02488 [math.NT], 2022-2023.
%e A353886 For k = 4, 4^2 + 4 + 1 = 21 = 3 * 7 is squarefree, so 4 belongs to this sequence.
%t A353886 Select[Range[0, 72], SquareFreeQ[#^2 + # + 1] &] (* _Amiram Eldar_, Dec 11 2023 *)
%o A353886 (PARI) is(k) = issquarefree(k^2 + k + 1);
%Y A353886 Cf. A000086, A002061, A005117, A353887 (corresponding squarefree numbers).
%K A353886 nonn,easy
%O A353886 1,3
%A A353886 _Rémy Sigrist_, May 09 2022