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#25 by Jon E. Schoenfield at Sat Jul 29 23:51:13 EDT 2017
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#24 by Jon E. Schoenfield at Sat Jul 29 23:51:01 EDT 2017
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| NAME
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Number of primitive solutions to n = x^2 + y^2 + z^2 (i.e. ., with gcd(x,y,z) = 1).
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| FORMULA
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Let h = number of classes of primitive binary quadratic forms, corresponding to the discriminant D= - = -n if n = 3 (mod 8), D= - = -4n if n = 1, 2, 5, 6 (mod 8) and let d_1 = 1/2, d_3 = 1/3, d_n = 1 otherwise. Then a(n) = 12 h d_n, if n= = 1, 2, 5, 6 (mod 8), 24 h d_n, if n = 3 (mod 8). (Grosswald)
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| STATUS
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approved
editing
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#23 by Charles R Greathouse IV at Sun Aug 28 18:18:35 EDT 2016
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| LINKS
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T. D. Noe, <a href="/A074590/b074590.txt">Table of n, a(n) for n= = 0..10000</a>
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Discussion
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Sun Aug 28
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| OEIS Server: https://oeis.org/edit/global/2560
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#22 by Michael Somos at Wed Jun 10 08:55:54 EDT 2015
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#21 by Michael Somos at Wed Jun 10 08:55:45 EDT 2015
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| MATHEMATICA
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a[ n_] := If[ n < 1, Boole[n == 0], Length[ @ Select[ {x, y, z} /. FindInstance[ n == x^2 + y^2 + z^2, {x, y, z}, Integers, 10^9], 1 == GCD @@ # &]]]; (* _ @@ # &]]; (* _Michael Somos_, May 21 2015 *)
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approved
editing
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Discussion
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Wed Jun 10
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| Michael Somos: Light edit.
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#20 by Michael Somos at Thu May 21 11:20:31 EDT 2015
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#19 by Michael Somos at Thu May 21 11:20:15 EDT 2015
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| EXAMPLE
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G.f. = 1 + 6*x + 12*x^2 + 8*x^3 + 24*x^5 + 24*x^6 + 24*x^9 + 24*x^10 + 24*x^11 + ...
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| MATHEMATICA
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a[ n_] := If[ n < 1, Boole[n == 0], Length[ Select[ {x, y, z} /. FindInstance[ n == x^2 + y^2 + z^2, {x, y, z}, Integers, 10^9], 1 == GCD @@ # &]]]; (* Michael Somos, May 21 2015 *)
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approved
editing
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Discussion
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Thu May 21
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| Michael Somos: Added more info.
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#18 by Charles R Greathouse IV at Thu Nov 21 13:11:39 EST 2013
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| MATHEMATICA
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a[n_] := (r = Reduce[ GCD[x, y, z] == 1 && n == x^2 + y^2 + z^2, {x, y, z}, Integers]; If[ r === False, 0, Length[ {ToRules[r]} ] ] ); a[0] = 1; Table[ a[n], {n, 0, 100}] (* From }] (* _Jean-François Alcover, _, Jan 13 2012 *)
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Discussion
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Thu Nov 21
| 13:11
| OEIS Server: https://oeis.org/edit/global/2066
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#17 by Charles R Greathouse IV at Fri May 10 12:45:04 EDT 2013
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| EXTENSIONS
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More terms from _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Dec 04 2002
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Discussion
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Fri May 10
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| OEIS Server: https://oeis.org/edit/global/1911
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#16 by T. D. Noe at Wed Oct 10 15:18:45 EDT 2012
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