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URL: https://oeis.org/A029703

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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
OFFSET
1,1
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 */
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