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%I M3291 #30 Jun 06 2019 08:51:03
%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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