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

%I A191411 #17 Feb 16 2025 08:33:14
%S A191411 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,
%T A191411 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,
%U A191411 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
%N A191411 Class number, k, of n; i.e., imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not squarefree (A005117).
%H A191411 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%H A191411 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A191411 f[n_] := If[! SquareFreeQ@ n, 0, NumberFieldClassNumber@Sqrt@ -n]; Array[f, 105]
%o A191411 (PARI) a(n) = if (! issquarefree(n), 0, qfbclassno(-n*if((-n)%4>1, 4, 1))); \\ _Michel Marcus_, Jul 08 2015
%Y A191411 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;
%Y A191411 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;
%Y A191411 a(n)=20: n/a; a(n)=21: A046018; a(n)=22: n/a;
%Y A191411 a(n)=23: A046020; a(n)=24: n/a; a(n)=25: A056987; etc.
%Y A191411 Cf. A191408, A191410.
%Y A191411 Cf. A000924 (without the zeros).
%K A191411 easy,nonn
%O A191411 1,5
%A A191411 _Robert G. Wilson v_, Jun 01 2011