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

79, 142, 223, 229, 254, 257, 321, 326, 359, 443, 469, 473, 659, 733, 761, 839, 934, 993, 1091, 1101, 1171, 1223, 1229, 1257, 1367, 1373, 1478, 1489, 1509, 1523, 1567, 1627, 1646, 1787, 1811, 1847, 1901, 1907, 1929, 1957, 1987, 2021, 2089, 2099, 2101, 2143, 2177, 2207, 2213

Offset: 1

Author

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

Keywords

• nonn

Examples

			79 is in the sequence because Z[sqrt(79)] has class number 3.
Z[sqrt(82)] has class number 4 and therefore 82 is not in the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to quadratic fields

Crossrefs

Cf. A003172, A029702, A029704-A029705, A218038-A218042.

Programs

Mathematica

Select[Range[2000], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] == 3 &] (* Alonso del Arte, Oct 17 2012 *)

PARI

A007947(n)={my(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i]); }
{ for (n=2, 10^4,
    if ( n!=A007947(n), next() );
    K = bnfinit(x^2 - n);
    if ( K.cyc == [3], print1( n, ", ") );
); }
/* Joerg Arndt, Oct 18 2012 */

Extensions

Missing initial term (79) added by Alonso del Arte, Oct 17 2012