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A093836 Numerator of A000328(n)/n^2, where A000328(n) is the number of lattice points (x,y) with x^2 + y^2 <= n^2.

%I A093836 #17 Feb 16 2025 08:32:53
%S A093836 5,13,29,49,81,113,149,197,253,317,377,49,529,613,709,797,53,1009,
%T A093836 1129,1257,1373,1517,1653,1793,1961,2121,763,2453,2629,2821,3001,3209,
%U A093836 3409,3625,3853,1351,4293,4513,4777,201,5261,5525,5789,6077,6361,6625
%N A093836 Numerator of A000328(n)/n^2, where A000328(n) is the number of lattice points (x,y) with x^2 + y^2 <= n^2.
%C A093836 First differs from A000328 at n=12: A000328(12) = 441, a(12) = 49.
%H A093836 Robert Israel, <a href="/A093836/b093836.txt">Table of n, a(n) for n = 1..10000</a>
%H A093836 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GausssCircleProblem.html">Gauss's Circle Problem</a>
%p A093836 N:= 100: # to get a(1) to a(N)
%p A093836 B:= Array(1..N);
%p A093836 for i from 0 to N do
%p A093836   for j from i while i^2 + j^2 <= N^2 do
%p A093836      v:= ceil(sqrt(i^2+j^2));
%p A093836      if [i,j] = [0,0] then m:= 1; v:= 1
%p A093836      elif i=0 or i=j then m:= 4
%p A093836      else m:= 8
%p A093836      fi;
%p A093836      B[v]:= B[v]+m;
%p A093836   od
%p A093836 od:
%p A093836 A000328:= ListTools:-PartialSums(convert(B,list)):
%p A093836 seq(numer(A000328[n]/n^2),n=1..N); # _Robert Israel_, May 28 2015
%Y A093836 Cf. A093837 (denominators), A000328, A093832.
%K A093836 nonn,frac
%O A093836 1,1
%A A093836 _Eric W. Weisstein_, Apr 17 2004
%E A093836 Definition edited by _Robert Israel_, May 28 2015