A034168
Disjoint discriminants (one form per genus) of type 2 (doubled).
Original entry on oeis.org
2, 6, 10, 22, 30, 42, 58, 70, 78, 102, 130, 190, 210, 330, 462
Offset: 1
Jonathan Borwein (jborwein(AT)cecm.sfu.ca), choi(AT)cecm.sfu.ca (Stephen Choi)
- J. M. Borwein and P. B. Borwein, Pi and the AGM, page 293.
- L. E. Dickson, Introduction to the theory of numbers, Dover, NY, 1929.
- J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016.
- J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016. [Cached copy, with permission]
- J. Borwein and K.-K. S. Choi, On the representations of xy+yz+zx, Experimental Mathematics, 9 (2000), 153-158.
- Experimental Mathematics, Home Page
-
noSol = {};
Do[lim = Ceiling[(n-2)/3]; found = False; Do[If[n > a*b && Mod[n - a*b, a+b] == 0 && Quotient[n - a*b, a+b] > b, found = True; Break[]], {a, 1, lim-1}, {b, a+1, lim}]; If[!found, AppendTo[noSol, n]], {n, 1000}];
Select[noSol, EvenQ[#] && SquareFreeQ[#]&] (* Jean-François Alcover, Jul 21 2022, after T. D. Noe in A000926 *)
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ok(n)={n%4==2 && issquarefree(n) && !select(t->t<>2, quadclassunit(-4*n).cyc)} \\ Andrew Howroyd, Jun 09 2018
A055745
Squarefree numbers not of form ab + bc + ca for 1 <= a <= b <= c (probably the list is complete).
Original entry on oeis.org
1, 2, 6, 10, 22, 30, 42, 58, 70, 78, 102, 130, 190, 210, 330, 462
Offset: 1
- Maohua Le, A note on positive integer solutions of the equation xy+yz+zx=n, Publ. Math. Debrecen 52 (1998) 159-165; Math. Rev. 98j:11016.
- J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016.
- J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016. [Cached copy, with permission]
- J. Borwein and K.-K. S. Choi, On the representations of xy+yz+zx, Experimental Mathematics, 9 (2000), 153-158.
-
solQ[n_, x_] := Reduce[1 <= y <= z && n == x*y + y*z + z*x, {y, z}, Integers] =!= False; solQ[n_] := Catch[xm = Ceiling[(n-1)/2]; For[x = 1, x <= xm, x++, Which[ solQ[n, x] === True, Throw[True], x == xm, Throw[False]]]] ; solQ[1] = False; Reap[ Do[ If[ SquareFreeQ[n], If[! solQ[n] , Print[n]; Sow[n]]], {n, 1, 500}]][[2, 1]] (* Jean-François Alcover, Jun 15 2012 *)
A034170
Disjoint discriminants (one form per genus) of type 1.
Original entry on oeis.org
5, 13, 21, 33, 37, 57, 85, 93, 105, 133, 165, 177, 253, 273, 345, 357, 385, 1365
Offset: 1
Jonathan Borwein (jborwein(AT)cecm.sfu.ca), Stephen Choi (choi(AT)cecm.sfu.ca)
- L. E. Dickson, Introduction to the theory of numbers, Dover, NY, 1929.
- J. M. Borwein and P. B. Borwein, Pi and the AGM, page 293.
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