A191411 Class number, k, of n; i.e., imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not squarefree (A005117).

1, 1, 1, 0, 2, 2, 1, 0, 0, 2, 1, 0, 2, 4, 2, 0, 4, 0, 1, 0, 4, 2, 3, 0, 0, 6, 0, 0, 6, 4, 3, 0, 4, 4, 2, 0, 2, 6, 4, 0, 8, 4, 1, 0, 0, 4, 5, 0, 0, 0, 2, 0, 6, 0, 4, 0, 4, 2, 3, 0, 6, 8, 0, 0, 8, 8, 1, 0, 8, 4, 7, 0, 4, 10, 0, 0, 8, 4, 5, 0, 0, 4, 3, 0, 4, 10, 6, 0, 12, 0, 2, 0, 4, 8, 8, 0, 4, 0, 0, 0, 14, 4, 5, 0, 8

Offset

1,5

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Class Number

Index entries for sequences related to quadratic fields

Mathematica

f[n_] := If[! SquareFreeQ@ n, 0, NumberFieldClassNumber@Sqrt@ -n]; Array[f, 105]

Prog

(PARI) a(n) = if (! issquarefree(n), 0, qfbclassno(-n*if((-n)%4>1, 4, 1))); \\ Michel Marcus, Jul 08 2015

Crossrefs

a(n)= 0: A013929; a(n)= 1: A003173; a(n)= 2: A005847; a(n)= 3: A006203; a(n)= 4: A046085; a(n)= 5: A046002; a(n)= 6: A055109; a(n)= 7: A046004; a(n)= 8: A055110; a(n)= 9: A046006; a(n)=10: A055111; a(n)=11: A046008; a(n)=12: n/a;

a(n)=13: A046010; a(n)=14: n/a; a(n)=15: A046012; a(n)=16: n/a; a(n)=17: A046014; a(n)=18: n/a; a(n)=19: A046016;

a(n)=20: n/a; a(n)=21: A046018; a(n)=22: n/a;

a(n)=23: A046020; a(n)=24: n/a; a(n)=25: A056987; etc.

Cf. A191408, A191410.

Cf. A000924 (without the zeros).

Sequence in context: A160806 A344447 A287385 * A133418 A181169 A029390

Adjacent sequences: A191408 A191409 A191410 * A191412 A191413 A191414

Keyword

easy,nonn

Author

Robert G. Wilson v, Jun 01 2011

Status

approved