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

%I A034168 #25 Apr 06 2024 09:03:11
%S A034168 2,6,10,22,30,42,58,70,78,102,130,190,210,330,462
%N A034168 Disjoint discriminants (one form per genus) of type 2 (doubled).
%D A034168 J. M. Borwein and P. B. Borwein, Pi and the AGM, page 293.
%D A034168 L. E. Dickson, Introduction to the theory of numbers, Dover, NY, 1929.
%H A034168 J. M. Borwein, <a href="https://carmamaths.org/resources/jon/OEIStalk.pdf">Adventures with the OEIS: Five sequences Tony may like</a>, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016.
%H A034168 J. M. Borwein, <a href="/A060997/a060997.pdf">Adventures with the OEIS: Five sequences Tony may like</a>, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016. [Cached copy, with permission]
%H A034168 J. Borwein and K.-K. S. Choi, <a href="https://projecteuclid.org/euclid.em/1046889597">On the representations of xy+yz+zx</a>, Experimental Mathematics, 9 (2000), 153-158.
%H A034168 Experimental Mathematics, <a href="http://www.emis.de/journals/EM/">Home Page</a>
%F A034168 Intersection of A005843 and A139826. - _Andrew Howroyd_, Jun 09 2018
%t A034168 noSol = {};
%t A034168 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}];
%t A034168 Select[noSol, EvenQ[#] && SquareFreeQ[#]&] (* _Jean-François Alcover_, Jul 21 2022, after _T. D. Noe_ in A000926 *)
%o A034168 (PARI) ok(n)={n%4==2 && issquarefree(n) && !select(t->t<>2, quadclassunit(-4*n).cyc)} \\ _Andrew Howroyd_, Jun 09 2018
%Y A034168 Cf. A000926, A005843, A034169, A055745, A139826. Subsequence of A025052.
%K A034168 nonn,fini,full,nice
%O A034168 1,1
%A A034168 Jonathan Borwein (jborwein(AT)cecm.sfu.ca), choi(AT)cecm.sfu.ca (Stephen Choi)