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A005472 Class numbers of cubic fields.
(Formerly M3291)
2

%I M3291

%S 1,1,1,1,1,1,1,4,7,4,4,4,7,4,13,7,19,7,7,7,19,19,19,16,31,19,28,19,49,

%T 31,28,31,64,43,37,127,61,52,52,52,49,100,37,112,64,67,61,76,61,76,61,

%U 61,112,76,73,67,133,91,223,169,73,112,100,169,91,121,175

%N Class numbers of cubic fields.

%C Class numbers of cubic fields with discriminants p^2, where p runs through the primes in A005471.

%C All terms are of the form x^2 + 3*y^2 (A003136). - _Colin Barker_, Nov 30 2014

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. J. Mathar, <a href="/A005472/b005472.txt">Table of n, a(n) for n = 1..100</a>

%H D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1974-0352049-8">The simplest cubic fields</a>, Math. Comp., 28 (1974), 1137-1152 (see Table 1 page 1140).

%o (PARI) A175282(n)={

%o local(a);

%o if(n==1,

%o return(1),

%o a=A175282(n-1)+1;

%o while(1,

%o if( isprime(a^2+3*a+9),

%o return(a),

%o a++

%o );

%o )

%o )

%o };

%o A005472(n)={

%o local(a,bnf,L,H);

%o if(n==1, return(1));

%o a=A175282(n);

%o bnf=bnfinit(x^3-a*x^2-(a+3)*x-1);

%o L=ideallist(bnf,1,2);

%o H=bnrclassnolist(bnf,L);

%o return(H[1][1]);

%o };

%o for(n=1,80, print1(A005472(n)," ") ); /* _R. J. Mathar_, Jun 06 2019 */

%K nonn

%O 1,8

%A _N. J. A. Sloane_

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)