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

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for sequences related to quadratic fields

Example

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.

Mathematica

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

Prog

(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 */

Crossrefs

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

Sequence in context: A141997 A107184 A250658 * A142082 A031890 A140008

Adjacent sequences: A029700 A029701 A029702 * A029704 A029705 A029706

Keyword

nonn

Author

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

Extensions

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

Status

approved