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%I #9 Jul 22 2021 07:02:06
%S 2,4,1,10,16,2,6,20,4,3,30,8,8,2,340,1,5,394,48,10,10,4,16,5,22,3040,
%T 2,46,70,12,12,74,50,6,64,26,6964,20,1,48670,96,4,2,100,3,7,10,178,30,
%U 302,198,1060,8,39,126,16,16,130,97684,8,25,502,6960,2,2136,86,4,340,9,106,160,1,18,164,5,9,20810
%N a(n) is twice the coefficient of 1 in the fundamental unit of Q(sqrt(A000037(n))) where A000037 lists the nonsquare numbers (Version 2).
%H S. R. Finch, <a href="https://web.archive.org/web/20160511035657/http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf">Class number theory</a>
%H Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FundamentalUnit.html">Fundamental Unit</a>.
%t nonSquares = Select[Range[72], !IntegerQ[Sqrt[#]]& ]; 2*NumberFieldFundamentalUnits[Sqrt[#]][[1, 2, 1]] & /@ nonSquares (* _Jean-François Alcover_, Nov 09 2012 *)
%o (PARI) for(n=1,30,if(!issquare(n),print1(abs(2*polcoeff(lift(bnfinit(x^2-n).fu[1]),0)),","))) /* _Ralf Stephan_, Sep 18 2013; updated by _Michel Marcus_, Jun 25 2020 */
%Y Cf. A000037, A346420, A048941, A048942.
%K nonn
%O 1,1
%A _Sean A. Irvine_