|
|
|
|
|
|
|
|
|
#25 by Jon E. Schoenfield at Sat Jul 29 23:51:13 EDT 2017
|
|
|
|
|
|
|
|
#24 by Jon E. Schoenfield at Sat Jul 29 23:51:01 EDT 2017
|
|
| NAME
|
Number of primitive solutions to n = x^2 + y^2 + z^2 (i.e. ., with gcd(x,y,z) = 1).
|
|
| FORMULA
|
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)
|
|
| STATUS
|
approved
editing
|
|
|
|
|
|
|
#23 by Charles R Greathouse IV at Sun Aug 28 18:18:35 EDT 2016
|
|
| LINKS
|
T. D. Noe, <a href="/A074590/b074590.txt">Table of n, a(n) for n= = 0..10000</a>
|
|
|
|
|
Discussion
|
| Sun Aug 28
| 18:18
| OEIS Server: https://oeis.org/edit/global/2560
|
|
|
|
|
|
|
#22 by Michael Somos at Wed Jun 10 08:55:54 EDT 2015
|
|
|
|
|
|
|
|
#21 by Michael Somos at Wed Jun 10 08:55:45 EDT 2015
|
|
| MATHEMATICA
|
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 *)
|
|
| STATUS
|
approved
editing
|
|
|
|
|
Discussion
|
| Wed Jun 10
| 08:55
| Michael Somos: Light edit.
|
|
|
|
|
|
|
#20 by Michael Somos at Thu May 21 11:20:31 EDT 2015
|
|
|
|
|
|
|
|
#19 by Michael Somos at Thu May 21 11:20:15 EDT 2015
|
|
| EXAMPLE
|
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 + ...
|
|
| MATHEMATICA
|
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 *)
|
|
| STATUS
|
approved
editing
|
|
|
|
|
Discussion
|
| Thu May 21
| 11:20
| Michael Somos: Added more info.
|
|
|
|
|
|
|
#18 by Charles R Greathouse IV at Thu Nov 21 13:11:39 EST 2013
|
|
| MATHEMATICA
|
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 *)
|
|
|
|
|
Discussion
|
| Thu Nov 21
| 13:11
| OEIS Server: https://oeis.org/edit/global/2066
|
|
|
|
|
|
|
#17 by Charles R Greathouse IV at Fri May 10 12:45:04 EDT 2013
|
|
| EXTENSIONS
|
More terms from _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Dec 04 2002
|
|
|
|
|
Discussion
|
| Fri May 10
| 12:45
| OEIS Server: https://oeis.org/edit/global/1911
|
|
|
|
|
|
|
#16 by T. D. Noe at Wed Oct 10 15:18:45 EDT 2012
|
|
|
|
|
|
|
