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 A060968 Number of solutions to x^2 + y^2 == 1 mod n. 18
 1, 2, 4, 8, 4, 8, 8, 16, 12, 8, 12, 32, 12, 16, 16, 32, 16, 24, 20, 32, 32, 24, 24, 64, 20, 24, 36, 64, 28, 32, 32, 64, 48, 32, 32, 96, 36, 40, 48, 64, 40, 64, 44, 96, 48, 48, 48, 128, 56, 40, 64, 96, 52, 72, 48, 128, 80, 56, 60, 128, 60, 64, 96, 128, 48, 96, 68, 128, 96, 64, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 L. Tóth, Counting solutions of quadratic congruences in several variables revisited, arXiv preprint arXiv:1404.4214, 2014 L. Toth, Counting Solutions of Quadratic Congruences in Several Variables Revisited, J. Int. Seq. 17 (2014) # 14.11.6. FORMULA Multiplicative, with a(2^e) = 2 if e = 1 or 2^(e+1) if e > 1, a(p^e) = (p-1)p^(e-1) if p == 1 (mod 4), a(p^e) = (p+1)p^(e-1) if p == 3 (mod 4). - David W. Wilson, Jun 19 2001 a(n) = n * product{ 1 - 1/p, p is prime, p | n and p = 1 mod 4 } * product{ 1 + 1/p, p is prime, p | n and p = 3 mod 4 } * {2, if 4 | n } - Ola Veshta (olaveshta(AT)my-deja.com), May 18 2001 EXAMPLE a(3) = 4 because the 4 solutions are: (0,1),(0,2),(1,0),(2,0) MATHEMATICA fa=FactorInteger; phi[p_, s_] := Which[Mod[p, 4] == 1, p^(s-1)*(p-1), Mod[p, 4]==3, p^(s-1)*(p+1), s==1, 2, True, 2^(s+1)]; phi=1; phi[n_] := Product[phi[fa[n][[i, 1]], fa[n][[i, 2]]], {i, Length[fa[n]]}]; Table[phi[n], {n, 1, 100}] PROG (PARI) a(n)=my(f=factor(n)[, 1]); n*prod(i=if(n%2, 1, 2), #f, if(f[i]%4==1, 1-1/f[i], 1+1/f[i]))*if(n%4, 1, 2) \\ Charles R Greathouse IV, Apr 16 2012 (Haskell) a060968 1 = 1 a060968 n = (if p == 2 then (if e == 1 then 2 else 2^(e+1)) else 1) *    (product \$ zipWith (*) (map (\q -> q - 2 + mod q 4) ps'')                           (zipWith (^) ps'' (map (subtract 1) es'')))    where (ps'', es'') = if p == 2 then (ps, es) else (ps', es')          ps'@(p:ps) = a027748_row n; es'@(e:es) = a124010_row n -- Reinhard Zumkeller, Aug 05 2014 CROSSREFS Cf. A060594, A087784. Cf. A027748, A124010. Sequence in context: A031401 A191333 A078479 * A323651 A151569 A016635 Adjacent sequences:  A060965 A060966 A060967 * A060969 A060970 A060971 KEYWORD nonn,easy,mult AUTHOR Ahmed Fares (ahmedfares(AT)my-deja.com), May 09 2001 STATUS approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)