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 A063725 Number of ordered pairs (x,y) of positive integers such that x^2 + y^2 = n. 29
 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS a(A018825(n))=0; a(A000404(n))>0; a(A081324(n))=1; a(A004431(n))>1. - Reinhard Zumkeller, Aug 16 2011 LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 FORMULA G.f.: (Sum_{m=1..inf} x^(m^2))^2. a(n) = ( A004018(n) - 2*A000122(n) + A000007(n) )/4. - Max Alekseyev, Sep 29 2012 G.f.: (theta_3(q) - 1)^2/4, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 08 2018 EXAMPLE a(5) = 2 from the solutions (1,2) and (2,1). MATHEMATICA nn = 100; t = Table[0, {nn}]; s = Sqrt[nn]; Do[n = x^2 + y^2; If[n <= nn, t[[n]]++], {x, s}, {y, s}]; Join[{0}, t] (* T. D. Noe, Apr 03 2011 *) PROG (Haskell) a063725 n =    sum \$ map (a010052 . (n -)) \$ takeWhile (< n) \$ tail a000290_list a063725_list = map a063725 [0..] -- Reinhard Zumkeller, Aug 16 2011 (PARI) a(n)=if(n==0, return(0)); my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4==1, f[i, 2]+1, f[i, 2]%2==0 || f[i, 1]==2)) - issquare(n) \\ Charles R Greathouse IV, May 18 2016 CROSSREFS Cf. A000404 (the numbers n that can be represented in this form). Cf. A000161, A063691, A063730, A025426, A000290, A010052. Column k=2 of A337165. Sequence in context: A329921 A092303 A329343 * A084888 A091400 A129448 Adjacent sequences:  A063722 A063723 A063724 * A063726 A063727 A063728 KEYWORD nonn AUTHOR N. J. A. Sloane, Aug 23 2001 STATUS approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)