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).

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, 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, 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

Offset: 1

Author

Robert G. Wilson v, Jun 01 2011

Keywords

• easy
• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Steven Arno, M. L. Robinson and Ferrel S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arithm. 83.4 (1998), 295-330
• Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
• C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
• Eric Weisstein's World of Mathematics, Class Number
• Index entries for sequences related to quadratic fields

Crossrefs

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.

Cf. A003657, A191408.

Programs

Mathematica

FundamentalDiscriminantQ[n_] := n != 1 && (Mod[n, 4] == 1 || !Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via Eric E. Weisstein *);
f[n_] := If[ !FundamentalDiscriminantQ@ -n, 0, NumberFieldClassNumber@ Sqrt@ -n]; Array[f, 105]

PARI

a(n)=if(isfundamental(-n),qfbclassno(-n),0) \\ Charles R Greathouse IV, Nov 20 2012