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A029703
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Q(sqrt(n)) has class number 3.
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4
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[2000], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] == 3 &] (* Alonso del Arte, Oct 17 2012 *)
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PROG
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(PARI)
A007947(n)={my(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i]); }
{ for (n=2, 10^4,
K = bnfinit(x^2 - n);
if ( K.cyc == [3], print1( n, ", ") );
); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it)
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EXTENSIONS
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STATUS
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approved
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