A034168 Disjoint discriminants (one form per genus) of type 2 (doubled).

2, 6, 10, 22, 30, 42, 58, 70, 78, 102, 130, 190, 210, 330, 462

Offset: 1

Author

Jonathan Borwein (jborwein(AT)cecm.sfu.ca), choi(AT)cecm.sfu.ca (Stephen Choi)

Keywords

• nonn
• fini
• full
• nice

References

• 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.

Links

• 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

Crossrefs

Cf. A000926, A005843, A034169, A055745, A139826. Subsequence of A025052.

Programs

Mathematica

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 *)

PARI

ok(n)={n%4==2 && issquarefree(n) && !select(t->t<>2, quadclassunit(-4*n).cyc)} \\ Andrew Howroyd, Jun 09 2018

Formula

Intersection of A005843 and A139826. - Andrew Howroyd, Jun 09 2018