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A029703 Q(sqrt(n)) has class number 3. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)