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A089269 Squarefree numbers congruent to 1 or 2 mod 4. 5
1, 2, 5, 6, 10, 13, 14, 17, 21, 22, 26, 29, 30, 33, 34, 37, 38, 41, 42, 46, 53, 57, 58, 61, 62, 65, 66, 69, 70, 73, 74, 77, 78, 82, 85, 86, 89, 93, 94, 97, 101, 102, 105, 106, 109, 110, 113, 114, 118, 122, 129, 130, 133, 134, 137, 138, 141, 142, 145, 146, 149, 154, 157 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 231-234.

A. Scholz and B. Schoeneberg, Einfuehrung 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

Cf. A000003, A005117, A039957, A003657.

Sequence in context: A212016 A212015 A255341 * A047440 A255055 A007674

Adjacent sequences:  A089266 A089267 A089268 * A089270 A089271 A089272

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 07 2003

EXTENSIONS

Entry revised by N. J. A. Sloane, May 28 2014

STATUS

approved

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Last modified May 19 02:29 EDT 2019. Contains 323377 sequences. (Running on oeis4.)