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A191410 Class number, k, of n, i.e.; imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not a fundamental discriminant (A003657).

%I A191410 #19 Feb 16 2025 08:33:14
%S A191410 0,0,1,1,0,0,1,1,0,0,1,0,0,0,2,0,0,0,1,2,0,0,3,2,0,0,0,0,0,0,3,0,0,0,
%T A191410 2,0,0,0,4,2,0,0,1,0,0,0,5,0,0,0,2,2,0,0,4,4,0,0,3,0,0,0,0,0,0,0,1,4,
%U A191410 0,0,7,0,0,0,0,0,0,0,5,0,0,0,3,4,0,0,6,2,0,0,2,0,0,0,8,0,0,0,0,0,0,0,5,6,0
%N A191410 Class number, k, of n, i.e.; imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not a fundamental discriminant (A003657).
%H A191410 Charles R Greathouse IV, <a href="/A191410/b191410.txt">Table of n, a(n) for n = 1..10000</a>
%H A191410 Steven Arno, M. L. Robinson and Ferrel S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arithm. 83.4 (1998), 295-330
%H A191410 Duncan A. Buell, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796.
%H A191410 C. Wagner, <a href="http://dx.doi.org/10.1090/S0025-5718-96-00722-3">Class Number 5, 6 and 7</a>, Math. Comput. 65, 785-800, 1996.
%H A191410 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%H A191410 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A191410 FundamentalDiscriminantQ[n_] := n != 1 && (Mod[n, 4] == 1 || !Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via Eric E. Weisstein *);
%t A191410 f[n_] := If[ !FundamentalDiscriminantQ@ -n, 0, NumberFieldClassNumber@ Sqrt@ -n]; Array[f, 105]
%o A191410 (PARI) a(n)=if(isfundamental(-n),qfbclassno(-n),0) \\ _Charles R Greathouse IV_, Nov 20 2012
%Y A191410 a(n)= 0:  n/a The complement of A003657; a(n)= 1: A014602; a(n)= 2: A014603; a(n)= 3: A006203; a(n)= 4: A013658; a(n)= 5: A046002; a(n)= 6: A046003; a(n)= 7: A046004; a(n)= 8: A046005; a(n)= 9: A046006; a(n)=10: A046007; a(n)=11: A046008; a(n)=12: A046009; a(n)=13: A046010; a(n)=14: A046011; a(n)=15: A046012; a(n)=16: A046013; a(n)=17: A046014; a(n)=18: A046015; a(n)=19: A046016; a(n)=20: A123563; a(n)=21: A046018; a(n)=22: A171724; a(n)=23: A046020; a(n)=24: A048925; a(n)=25: A056987; etc.
%Y A191410 Cf. A003657, A191408.
%K A191410 easy,nonn
%O A191410 1,15
%A A191410 _Robert G. Wilson v_, Jun 01 2011