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

1,1

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

Table of n, a(n) for n=1..15.

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A140775 A077064 A080715 * A055745 A371283 A182000

Adjacent sequences: A034165 A034166 A034167 * A034169 A034170 A034171

Keyword

nonn,fini,full,nice

Author

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

Status

approved