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 A285022 #31 Feb 27 2020 17:54:17
%S A285022 820,1276,1926,2080,2640,3160,3186,3250,4446,4720,4930,5370,6006,6546,
%T A285022 7386,7450,7476,9066,9276,10626,10836,13146,13300,15640,15666,16056,
%U A285022 16060,16446,17020,17466,17550,17766,18040,18910,19176,19230,19416,20736,21000,21246
%N A285022 Numbers n such that A002088(n) < 3n^2/Pi^2.
%C A285022 James Joseph Sylvester conjectured in 1883 that A002088(n) > 3n^2/Pi^2 for all n.
%C A285022 M. L. N. Sarma found the first counterexample, 820, in 1936.
%C A285022 Paul Erdős and Harold N. Shapiro proved in 1951 that A002088(n)- 3n^2/Pi^2 changes signs at infinitely many values of n, thus this sequence is infinite.
%C A285022 R. A. MacLeod proved in 1987 that A002088(n)/n^2 - 3/Pi^2 has a minimum at the second term, 1276.
%D A285022 Sukumar Das Adhikari, The Average Behaviour of the Number of Solutions of a Diophantine Equation and an Averaging Technique, Number Theory: Diophantine, Computational, and Algebraic Aspects: Proceedings of the International Conference Held in Eger, Hungary, July 29-August 2, 1996. Walter de Gruyter, 1998.
%D A285022 Władysław Narkiewicz, Rational Number Theory in the 20th Century, Springer London, 2012, p. 215.
%D A285022 M. L. N. Sarma, On the Error Term in a Certain Sum, Proceedings of the Indian Academy of Sciences, Section A, Vol. 3, No. 1 (1936), pp. 338-338.
%H A285022 Amiram Eldar and Giovanni Resta, <a href="/A285022/b285022.txt">Table of n, a(n) for n = 1..10000</a> (first 97 terms from Amiram Eldar)
%H A285022 Paul Erdős and Harold N. Shapiro, <a href="http://dx.doi.org/10.4153/CJM-1951-043-3">On the Changes of Sign of a Certain Error Function</a>, Canadian Journal of Mathematics, Vol. 3 (1951), pp. 375-385.
%H A285022 R. A. MacLeod, <a href="https://doi.org/10.1112/jlms/s1-42.1.652">The Minimum of Phi(x)/x^2</a>, Journal of the London Mathematical Society, Vol. 1, No. 1 (1967), pp. 652-660.
%H A285022 James Joseph Sylvester, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k3052k/f463.item">Note sur le théoreme de Legendre citée dans une note insérée dans les Comptes rendus</a>, Comptes rendus hebdomadaires des seances de l'Academie des sciences, Vol. 46 (1883), pp. 463-465.
%H A285022 James Joseph Sylvester, <a href="http://dx.doi.org/10.1080/14786448308627346">On the Number of Fractions Contained in any "Farey series" of which the Limiting Number is Given</a>, Philosophical Magazine, Series 5, Vol. 15, No. 94 (1883), pp. 251-257.
%e A285022 A002088(820) = 204376, 3*820^2/(Pi^2) = 204385.091643... > 204376, thus 820 is in this sequence.
%p A285022 F:= ListTools:-PartialSums(map(numtheory:-phi, [$1..30000])):
%p A285022 select(t -> is(F[t] < 3*t^2/Pi^2), [$1..30000]); # _Robert Israel_, Apr 21 2017
%t A285022 s = 0; k = 1; lst = {}; While[k < 50001, s = s + EulerPhi@k; If[s*Pi^2 < 3 k^2, AppendTo[lst, k]]; k++]; lst
%Y A285022 Cf. A000010, A002088.
%K A285022 nonn
%O A285022 1,1
%A A285022 _Amiram Eldar_, Apr 08 2017