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%I A001481 M0968 N0361
%S A001481 0,1,2,4,5,8,9,10,13,16,17,18,20,25,26,29,32,34,36,37,40,41,45,49,50,52,
%T A001481 53,58,61,64,65,68,72,73,74,80,81,82,85,89,90,97,98,100,101,104,106,109,
%U A001481 113,116,117,121,122,125,128,130,136,137,144,145,146,148,149,153,157,160
%N A001481 Numbers that are the sum of 2 nonnegative squares.
%C A001481 Numbers n such that n = x^2 + y^2 has a solution in nonnegative integers 
               x, y.
%C A001481 Also, numbers whose cubes are the sum of 2 squares. - Artur Jasinski 
               (grafix(AT)csl.pl), Nov 21 2006 (Cf. A125110.)
%C A001481 Terms are the squares of smallest radii of circles covering (on a square 
               grid) a number of points equal to the terms of A057961. - Philippe 
               Lallouet (philip.lallouet(AT)wanadoo.fr), Apr 16 2007. [Comment corrected 
               by T. D. Noe (noe(AT)sspectra.com), Mar 28 2008]
%D A001481 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", 
               Springer-Verlag, p. 106.
%D A001481 D. Cox, "Primes of Form x^2 + n y^2", Wiley, 1989.
%D A001481 L. Euler, (E388) Vollstaendige Anleitung zur Algebra, Zweiter Theil, 
               reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 
               1, p. 417.
%D A001481 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 98-104.
%D A001481 G. H. Hardy, Ramanujan, pp. 60-63.
%D A001481 Peter Shiu, Counting Sums of Two Squares: The Meissel-Lehmer Method", 
               Mathematics of Computation 47 (1986), 351-360.
%D A001481 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001481 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001481 A. van Wijngaarden, A table of partitions into two squares with an application 
               to rational triangles, Proceedings of the Koninklijke Nederlandse 
               Akademie van Wetenschappen, Series A, 53 (1950), 869-875.
%H A001481 T. D. Noe, <a href="b001481.txt">Table of n, a(n) for n = 1..10000</a>
%H A001481 M. Baake, U. Grimm, D. Joseph and P. Repetowicz, <a href="http://arXiv.org/
               abs/math.MG/9907156">Averaged shelling for quasicrystals</a>
%H A001481 H. Bottomley, <a href="a001481.gif">Illustration of initial terms</a>
%H A001481 R. T. Bumby, <a href="http://www.math.rutgers.edu/~bumby/squares1.pdf">
               Sums of four squares</a>, in Number theory (New York, 1991-1995), 
               1-8, Springer, New York, 1996.
%H A001481 J. Butcher, <a href="http://www.math.auckland.ac.nz/~butcher/miniature/
               miniature7.pdf">Quadratic residues and sums of two squares</a>
%H A001481 J. Butcher, <a href="http://www.math.auckland.ac.nz/~butcher/miniature/
               miniature14.pdf">Sums of two squares revisited</a>
%H A001481 L. Euler, <a href="http://www.mathematik.uni-bielefeld.de/~sieben/euler/
               euler_2.djvu">Vollstaendige Anleitung zur Algebra, Zweiter Teil</
               a>.
%H A001481 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/lr/lr.html">
               Landau-Ramanujan Constant</a>
%H A001481 S. R. Finch, <a href="http://algo.inria.fr/csolve/fermat.pdf">On a Generalized 
               Fermat-Wiles Equation</a>
%H A001481 W. A. Stein, <a href="http://modular.fas.harvard.edu/edu/Fall2001/124/
               lectures/lecture21/lecture21">Quadratic Forms:Sums of Two Squares</
               a>
%H A001481 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SquareNumber.html">Link to a section of The World of Mathematics 
               (1).</a>
%H A001481 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GeneralizedFermatEquation.html">Link to a section of The World of 
               Mathematics (2).</a>
%H A001481 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Landau-RamanujanConstant.html">Landau-Ramanujan Constant</a>
%H A001481 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~twosquares.en.html">
               Two squares</a>
%H A001481 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%H A001481 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A001481 n = square * 2^{0 or 1} * {product of distinct primes == 1 (mod 4)}.
%F A001481 The number of integers <N that are sums of two squares is asymptotic 
               to constant*N/sqrt(log(N)).
%F A001481 Closed under multiplication. - David W. Wilson, Dec 20 2004
%F A001481 lim n->inf a(n)/n = inf.
%F A001481 Nonzero terms in expansion of Dirichlet series Product_p (1-(Kronecker(m, 
               p)+1)*p^(-s)+Kronecker(m, p)*p^(-2s))^(-1) for m = -1.
%p A001481 readlib(issqr): for n from 0 to 160 do for k from 0 to floor(sqrt(n)) 
               do if issqr(n-k^2) then printf(`%d,`,n); break fi: od: od:
%o A001481 (PARI) isA001481(n) = {local(x,r);x=0;r=0;while(x<=sqrt(n)&r==0,if(issquare(n-x^2),
               r=1);x++);r} [From Michael Porter (michael_b_porter(AT)yahoo.com), 
               Oct 31 2009]
%Y A001481 Complement of A022544. Cf. A004018, A000161, A002654, A064533.
%Y A001481 A000404 gives another version.
%Y A001481 Cf. A002828, A000378, A025284-A025320, A125110.
%Y A001481 Subset of A091072.
%Y A001481 Sequence in context: A084581 A121996 A091072 this_sequence A034026 A125022 
               A069011
%Y A001481 Adjacent sequences: A001478 A001479 A001480 this_sequence A001482 A001483 
               A001484
%K A001481 nonn,nice,easy,core
%O A001481 1,3
%A A001481 N. J. A. Sloane (njas(AT)research.att.com).

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