OFFSET
1,2
COMMENTS
a(n) = one-fourth of the (negated) fundamental even discriminants D := b^2-4*a*c<0 of positive definite binary quadratic forms F=a*x^2+b*x*y+c*y^2. See A039957 for the odd numbers and A003657 for the combined even and odd numbers.
The asymptotic density of this sequence is 4/Pi^2 (A185199). - Amiram Eldar, Feb 23 2021
REFERENCES
Duncan A. Buell, Binary Quadratic Forms, Springer-Verlag, NY, 1989, pp. 231-234.
Arnold Scholz and Bruno Schoeneberg, Einführung in die Zahlentheorie, 5. Aufl., de Gruyter, Berlin, New York, 1973, Ch. 30.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..10000
MATHEMATICA
Select[Range[200], MemberQ[{1, 2}, Mod[#, 4]]&& SquareFreeQ[#]&] (* Vincenzo Librandi, Oct 20 2017 *)
PROG
(Magma) [n: n in [1..200] | IsSquarefree(n) and n mod 4 in [1, 2]]; // Vincenzo Librandi, Oct 20 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Nov 07 2003
EXTENSIONS
Entry revised by N. J. A. Sloane, May 28 2014
STATUS
approved