A346419 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).

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, 2, 46, 70, 12, 12, 74, 50, 6, 64, 26, 6964, 20, 1, 48670, 96, 4, 2, 100, 3, 7, 10, 178, 30, 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

Offset: 1

Author

Sean A. Irvine

Keywords

• nonn

Links

• S. R. Finch, Class number theory
• Steven R. Finch, Class number theory [Cached copy, with permission of the author]
• Eric Weisstein's World of Mathematics, Fundamental Unit.

Crossrefs

Cf. A000037, A346420, A048941, A048942.

Programs

Mathematica

nonSquares = Select[Range[72], !IntegerQ[Sqrt[#]]& ]; 2*NumberFieldFundamentalUnits[Sqrt[#]][[1, 2, 1]] & /@ nonSquares (* Jean-François Alcover, Nov 09 2012 *)

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 */