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A029703 Q(sqrt(n)) has class number 3.

%I A029703 #16 May 13 2013 01:54:04
%S A029703 79,142,223,229,254,257,321,326,359,443,469,473,659,733,761,839,934,
%T A029703 993,1091,1101,1171,1223,1229,1257,1367,1373,1478,1489,1509,1523,1567,
%U A029703 1627,1646,1787,1811,1847,1901,1907,1929,1957,1987,2021,2089,2099,2101,2143,2177,2207,2213
%N A029703 Q(sqrt(n)) has class number 3.
%H A029703 Charles R Greathouse IV, <a href="/A029703/b029703.txt">Table of n, a(n) for n = 1..10000</a>
%H A029703 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%e A029703 79 is in the sequence because Z[sqrt(79)] has class number 3.
%e A029703 Z[sqrt(82)] has class number 4 and therefore 82 is not in the sequence.
%t A029703 Select[Range[2000], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] == 3 &] (* _Alonso del Arte_, Oct 17 2012 *)
%o A029703 (PARI)
%o A029703 A007947(n)={my(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i]); }
%o A029703 { for (n=2, 10^4,
%o A029703     if ( n!=A007947(n), next() );
%o A029703     K = bnfinit(x^2 - n);
%o A029703     if ( K.cyc == [3], print1( n, ", ") );
%o A029703 ); }
%o A029703 /* _Joerg Arndt_, Oct 18 2012 */
%Y A029703 Cf. A003172, A029702, A029704-A029705, A218038-A218042.
%K A029703 nonn
%O A029703 1,1
%A A029703 Paolo Dominici (pl.dm(AT)libero.it)
%E A029703 Missing initial term (79) added by _Alonso del Arte_, Oct 17 2012