A029702 - OEIS

%I #22 Aug 25 2014 13:09:26

%S 10,15,26,30,34,35,39,42,51,55,58,65,66,70,74,78,85,87,91,95,102,105,

%T 106,110,111,114,115,119,122,123,138,143,146,154,155,159,165,174,178,

%U 182,183,185,186,187,190,194,202,203,205,215,218,221,222,230,238,246

%N Q(sqrt(n)) has class number 2.

%C Smallest term that is in A146209 but not this sequence is 79, since Q(sqrt(79)) has class number 3. - _Alonso del Arte_, Aug 25 2014

%H Charles R Greathouse IV, <a href="/A029702/b029702.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%t Select[Range[246], SquareFreeQ[#] && NumberFieldClassNumber@Sqrt[#] == 2 &] (* _Arkadiusz Wesolowski_, Oct 22 2012 *)

%o (PARI)

%o A007947(n)={my(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i]); }

%o { for (n=2, 10^3,

%o     if ( n!=A007947(n), next() );

%o     K = bnfinit(x^2 - n);

%o     if ( K.cyc == [2], print1( n, ", ") );

%o ); }

%o /* _Joerg Arndt_, Oct 18 2012 */

%Y Cf. A003172, A029703-A029705, A218038-A218042.

%K nonn

%O 1,1

%A Paolo Dominici (pl.dm(AT)libero.it)