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 A087784 Number of solutions to x^2 + y^2 + z^2 = 1 mod n. 12
 1, 4, 6, 24, 30, 24, 42, 96, 54, 120, 110, 144, 182, 168, 180, 384, 306, 216, 342, 720, 252, 440, 506, 576, 750, 728, 486, 1008, 870, 720, 930, 1536, 660, 1224, 1260, 1296, 1406, 1368, 1092, 2880, 1722, 1008, 1806, 2640, 1620, 2024, 2162, 2304, 2058, 3000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 László Tóth, Counting solutions of quadratic congruences in several variables revisited, arXiv preprint arXiv:1404.4214 [math.NT], 2014. László Tóth, Counting Solutions of Quadratic Congruences in Several Variables Revisited, Journal of Integer Sequences, 17 (2014), Article 14.11.6. FORMULA a(n) = n^2 * (3/2 if 4|n) * Product_{primes p == 1 mod 4 dividing n} (1+1/p) * Product_{primes p == 3 mod 4 dividing n} (1-1/p). - Bjorn Poonen, Dec 09 2003 Sum_{k=1..n} a(k) ~ c * n^3 + O(n^2 * log(n)), where c = 36*G/Pi^4 = 0.338518..., where G is Catalan's constant (A006752) (Tóth, 2014). - Amiram Eldar, Oct 18 2022 MATHEMATICA Table[With[{f = FactorInteger[n][[All, 1]]}, Apply[Times, Map[1 + 1/# &, Select[f, Mod[#, 4] == 1 &]]] Apply[Times, Map[1 - 1/# &, Select[f, Mod[#, 4] == 3 &]]] (1 + Boole[Divisible[n, 4]]/2) n^2] - Boole[n == 1], {n, 50}] (* Michael De Vlieger, Feb 15 2018 *) PROG (PARI) a(n) = {my(f=factor(n)); if ((n % 4), 1, 3/2)*n^2*prod(k=1, #f~, p = f[k, 1]; m = p % 4; if (m==1, 1+1/p, if (m==3, 1-1/p, 1))); } \\ Michel Marcus, Feb 14 2018 CROSSREFS Cf. A006752, A060968, A087687, A208895, A264083. Sequence in context: A237748 A359863 A326233 * A174197 A071224 A305381 Adjacent sequences: A087781 A087782 A087783 * A087785 A087786 A087787 KEYWORD nonn,mult AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 06 2003 EXTENSIONS More terms from David Wasserman, Jun 17 2005 STATUS approved

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Last modified June 15 06:51 EDT 2024. Contains 373402 sequences. (Running on oeis4.)