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 A014200 #38 Aug 03 2025 09:20:52
%S A014200 0,1,2,2,3,5,5,5,6,7,9,9,9,11,11,11,12,14,15,15,17,17,17,17,17,20,22,
%T A014200 22,22,24,24,24,25,25,27,27,28,30,30,30,32,34,34,34,34,36,36,36,36,37,
%U A014200 40,40,42,44,44,44,44,44,46
%N A014200 Number of solutions to x^2 + y^2 <= n, excluding (0,0), divided by 4.
%C A014200 From _Ant King_, Mar 15 2013: (Start)
%C A014200 The terms of this sequence give a running total of the excess of the 4k + 1 divisors of the natural numbers (from 1 through to n) over their 4k + 3 divisors.
%C A014200 To see how good the approximation n * Pi/4 is to a(n), note that a(10^6) = 785387 whereas 10^6 * Pi/4 rounds to 785398. (End)
%H A014200 Seiichi Manyama, <a href="/A014200/b014200.txt">Table of n, a(n) for n = 0..10000</a>
%F A014200 a(n) = A014198(n) / 4.
%F A014200 Limit_{n->infinity} a(n)/n = Pi/4 = A003881.
%F A014200 a(n) = n - floor(n/3) + floor(n/5) - floor(n/7) + floor(n/9) - floor(n/11) + ... - Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 28 2003
%F A014200 G.f.: (1/(1 - x))*Sum_{k>=1} x^k/(1 + x^(2*k)). - _Ilya Gutkovskiy_, Dec 23 2016
%t A014200 1/4*Prepend[SquaresR[2,#]&/@Range[58],0]//Accumulate (* _Ant King_, Mar 15 2013 *)
%o A014200 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, kronecker(-4, k/d))); \\ _Seiichi Manyama_, Dec 18 2021
%Y A014200 Cf. A014198, A059851, A101455.
%Y A014200 Partial sums of A002654.
%K A014200 nonn
%O A014200 0,3
%A A014200 _N. J. A. Sloane_