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Numbers n such that Q(sqrt(-n)) has class number 4.
6

%I #26 May 25 2024 14:36:22

%S 14,17,21,30,33,34,39,42,46,55,57,70,73,78,82,85,93,97,102,130,133,

%T 142,155,177,190,193,195,203,219,253,259,291,323,355,435,483,555,595,

%U 627,667,715,723,763,795,955,1003,1027,1227,1243,1387,1411,1435,1507,1555

%N Numbers n such that Q(sqrt(-n)) has class number 4.

%C Contains 54 numbers [Arno, Theorem 7], ..., 1387, 1411, 1435, 1507 and 1555. [_R. J. Mathar_, May 01 2010]

%H Steven Arno, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa60/aa6042.pdf">The imaginary quadratic fields of class number 4</a>, Acta Arithm. vol 60 issue 4 (1991).

%H Steven Arno, M. L. Robinson, Ferrell S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arith. 83 (1998) 295-330.

%H Keith Matthews, <a href="http://www.numbertheory.org/classnos/">Tables of imaginary quadratic fields with small class numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%o (PARI) \\ See A005847

%Y See A003173, A005847, A006203, A046085, A046002, A055109, A046004, A055110, A046006, A055111 for class numbers 1 through 10.

%K nonn,fini,full

%O 1,1

%A _N. J. A. Sloane_, Jun 16 2000